Design method of graphite heating element of bismuth refining vacuum furnace and vacuum furnace

Abstract

The application belongs to the field of non-ferrous metallurgy equipment, and particularly discloses a design method of a graphite heating body of a bismuth refining vacuum furnace and the vacuum furnace. The design method comprises the following steps: S1, calculating a target temperature gradient required by each layer of evaporation tray in the vacuum furnace based on the thermodynamic phase equilibrium principle according to raw materials and target product purity; S2, deriving a functional relationship S=f(h) of the cross-sectional area S of the graphite heating body changing with the height h by combining the Joule's law, the resistance law and the radiation law; and S3, processing the variable cross-section graphite heating body according to the function. The vacuum furnace using the method has a variable cross-section structure. The application optimizes the shape of the heating body, accurately matches the heat supply with the component change requirement in the evaporation process of the material, ensures that the bismuth and silver content in the distillation meets the standard, significantly reduces the energy consumption, and improves the process adaptability.

Description

Technical Field

[0001] This invention relates to the field of non-ferrous metal metallurgical equipment technology, specifically to a vacuum furnace for the silver removal process of refined bismuth vacuum distillation, and particularly to an optimized design method for the graphite heating element in the vacuum furnace. Background Technology

[0002] Bismuth, a key non-ferrous metal in the electronics, pharmaceutical, and semiconductor fields, requires extremely high purity. The national standard for #1 Bi requires a silver (Ag) content of ≤40g / t. Industrially, vacuum distillation is commonly used to separate bismuth-silver alloys. Its core principle is to utilize the vapor pressure difference between bismuth and silver under the same conditions, causing bismuth, as the easily evaporable component, to evaporate, thus achieving separation from the more difficult-to-evaporate silver.

[0003] Existing technologies commonly employ multi-stage stacked internally heated and externally cooled vacuum furnaces. This furnace type includes horizontally stacked annular evaporation pans, a graphite heating element running through them, and a surrounding condensation system. Molten bismuth-silver alloy flows in from the topmost evaporation pan and sequentially through each layer. Under vacuum and heating conditions, bismuth continuously evaporates, condenses, and is collected, while silver continuously accumulates in the residue.

[0004] Currently, the core flaw of this technical solution lies in the fact that its graphite heating element typically adopts a cylindrical structure with a uniform cross-section. This design results in each evaporation plate receiving essentially the same amount of thermal radiation power, which cannot match the dynamic changes in the composition of the material (decreasing Bi content and increasing Ag content) during distillation. Specific problems are as follows: Distilled bismuth is prone to exceeding silver content limits: As evaporation proceeds, the silver content of the molten bismuth in the lower evaporation pan increases. According to the phase equilibrium theory of vacuum distillation, under isothermal heating, the silver content in the vapor generated in the lower layer will increase significantly. When this high-silver vapor mixes with the low-silver vapor in the upper layer, it can easily lead to the silver content in the final collected distilled bismuth approaching or exceeding the limit of 30 g / t.

[0005] Significant energy waste: To ensure production capacity, overall power needs to be increased to bring each layer (especially the lower layer) to the required temperature. However, the bismuth content in the lower layer material is already low, reducing the required heat for evaporation and leading to an oversupply of heat in the lower layer, resulting in energy waste.

[0006] Poor process adaptability: When the silver content of the raw materials fluctuates, the uniform cross-section design cannot flexibly adjust the heat distribution of each layer. To ensure product quality, it is often necessary to sacrifice production capacity or increase energy consumption, resulting in poor process adaptability.

[0007] Therefore, there is an urgent need for a design method for graphite heating elements that can match the heat of each layer according to changes in material composition, so as to improve energy utilization efficiency and process adaptability while ensuring that the purity of distilled bismuth meets the standards. Summary of the Invention

[0008] The purpose of this invention is to provide a method for designing a graphite heating element for a bismuth refining vacuum furnace and a vacuum furnace using this method, so as to solve at least one technical problem existing in the background art.

[0009] To achieve the above objectives, the technical solution adopted by the present invention is as follows: A method for designing a graphite heating element for a bismuth refining vacuum furnace, wherein the vacuum furnace has n layers of annular evaporation disks stacked from top to bottom, and the graphite heating element is vertically inserted through the center of each evaporation disk layer. The design method includes the following steps: S1. Determine the target temperature T for each evaporator layer. i Based on the initial molar ratio of silver to bismuth in the raw material melt x0, the target molar ratio of silver to bismuth in the distilled bismuth y0, and the final molar ratio of silver to bismuth in the residue x n Combining the Clausius-Clapeyron equation and the phase equilibrium equation for vacuum distillation, the molar ratio y of silver to bismuth in the vapor produced by each evaporation pan was calculated. i When all values ​​are equal to y0, the required temperature T for each evaporation plate is... i Where i is the evaporator disk layer number, from top to bottom i=1 to n, and T1>T2>…>T n ; S2. Establish the functional relationship between the cross-sectional area S of the graphite heating element and its height h: based on the discrete temperature point T obtained in step S1. i and the corresponding evaporator center height h i By combining Joule's law, the law of resistance, and the Stefan-Boltzmann radiation law, a continuous functional relationship S=f(h) is obtained for the cross-sectional area S of the graphite heating element along its height h, where the height h is taken as the reference zero point at the center of the lowest evaporation disk. The function f(h) satisfies that when a constant working current I is applied to the entire graphite heating element, the local thermal radiation power of the heating element at height h matches the target temperature T(h) required by the evaporation disk at the corresponding height. S3. Manufacturing a graphite heating element: Based on the functional relationship S=f(h) obtained in step S2, manufacture a graphite heating element whose cross-sectional area varies continuously or segmentally along its height direction.

[0010] Preferably, in step S1, the target temperature T i Determined by the following formula: y0 Where y0 is the target value of the Ag / Bi molar ratio in distilled bismuth, and x i γ is the molar ratio of Ag / Bi in the melt in the i-th evaporation pan. Ag and γ Bi Activity coefficients of Ag and Bi, ΔS Ag-vap and ΔS Bi-vap Molar evaporation entropy of Ag and Bi, ΔHAg-vap and ΔH Bi-vap Here, denoted as the molar enthalpy of vaporization for Ag and Bi, respectively, and R is the ideal gas constant with a value of 8.314 J / (mol·K).

[0011] Preferably, in step S2, the cross-sectional area S of the graphite heating element at the height position of the i-th evaporation disk is... i Determined by the following formula: Where I is the design operating current, ρ0 is the resistivity of the graphite material at the reference temperature T'0, and T ' 0 represents the reference temperature for graphite resistivity (298 K), L represents the length of the heating element unit corresponding to the distance between adjacent evaporation disks, α represents the temperature coefficient of resistance of the graphite material, and T represents the temperature coefficient of resistance of the graphite material. i Let T be the temperature of the evaporator plate in the i-th layer. ' i The temperature of the graphite heating element corresponding to the evaporation disk of the i-th layer; C=k ε is the emissivity of the graphite heating element, σ is the Stefan-Boltzmann constant, A is the radiating area of ​​the graphite heating element at the corresponding height, and k is a correction factor with a value ranging from 0.85 to 0.95. T' i =T i .

[0012] Preferably, in step S2, the calculated discrete data points (S) are processed... i h i The continuous function relationship S=f(h) is obtained by mathematical fitting. The function form used for fitting includes, but is not limited to, quadratic polynomial, piecewise linear function or exponential function.

[0013] Preferably, the functional relationship S=f(h) obtained in step S2 is a quadratic function: S(h)=a-bh-ch 2 Where a, b, and c are constants determined based on specific process parameters, physical property parameters, and electrothermal parameters, 0 ≤ h ≤ H, and H is the height corresponding to the uppermost evaporation plate.

[0014] Preferably, the functional relationship S=f(h) satisfies the following: the cross-sectional area S of the graphite heating element decreases as the height h increases.

[0015] A bismuth refining vacuum furnace includes a furnace body, n annular evaporation plates disposed within the furnace body, a graphite heating element vertically inserted at the center of each evaporation plate, and a condensation collection system. The cross-sectional area of ​​the graphite heating element varies continuously or segmentally along its height direction, and its variation law conforms to the functional relationship S=f(h) determined by the design method.

[0016] Preferably, the cross-sectional area S of the graphite heating element decreases with increasing height h.

[0017] Preferably, n is 30 to 40 layers.

[0018] Preferably, the graphite heating element is made of high-density isostatically pressed graphite.

[0019] Compared with the prior art, the beneficial effects of the present invention are as follows: This invention employs a gradient temperature field design that promotes bismuth evaporation at a high temperature in the upper layer and inhibits silver volatilization at a low temperature in the lower layer. This ensures that the silver content in the steam generated by each evaporation plate is low, thereby guaranteeing that the silver content of the final collected distilled bismuth is consistently below 30 g / t, which is superior to the national standard 1#Bi requirement.

[0020] The variable cross-section design of this invention enables precise matching of heat supply with material evaporation requirements, avoiding the excess heat in the lower layers that occurs with a constant cross-section design. Practical applications show that, under the same raw material and production capacity conditions, energy savings can be achieved (e.g., energy consumption is reduced to approximately 82.8% of the energy consumption of the original constant cross-section design).

[0021] This invention provides a flexible design basis for different silver contents in raw materials. By adjusting the design parameters, high production capacity can be maintained or energy consumption can be further optimized while ensuring product quality, demonstrating strong process adaptability.

[0022] This invention is based on mature thermodynamics and heat transfer principles. Through rigorous mathematical derivation, the design goal is transformed into a specific, manufacturable geometric shape. It has sufficient theoretical basis and high engineering feasibility. Attached Figure Description

[0023] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used together with the embodiments of the invention to explain the invention and do not constitute a limitation thereof.

[0024] In the attached diagram: Figure 1 This is a graph showing the cross-sectional area S of the graphite heating element as a function of height h in an embodiment of the present invention. Detailed Implementation

[0025] In a first aspect, the present invention provides a method for designing a graphite heating element for a bismuth refining vacuum furnace.

[0026] The vacuum furnace has n layers of annular evaporation disks stacked from top to bottom, with graphite heating elements vertically inserted at the center of each evaporation disk layer. The core of the design methodology lies in translating the process objective into a physical design, specifically including the following three steps: S1. Determine the target temperature gradient for each evaporation plate.

[0027] The purpose of this step is to calculate the temperature required for each evaporation plate to achieve the state where "the silver content in the steam evaporated from each layer is exactly equal to the final product requirement".

[0028] Specifically: Based on the initial molar ratio of Ag / Bi in the raw material (denoted as x0 in molar ratio), the target molar ratio of silver to bismuth in distilled bismuth (y0), and the final molar ratio of silver to bismuth in the residue (x n Iterative calculations were performed by combining the Clausius-Clapeyron equation, the vacuum distillation phase equilibrium theory, and Raoult's law.

[0029] Clausius-Clapeyron equations: in: For molar enthalpy of vaporization, , where is the molar entropy of evaporation, and both are usually considered constants at a given temperature; T is the temperature of the evaporating pan (unit: K), P0 represents the standard atmospheric pressure, which is 101325 Pa, and R is the ideal gas constant (8.314 J / (mol·K)).

[0030] For Bi-Ag alloy melts, the Ag / Bi molar ratio y in the vapor i Compared with the Ag / Bi molar ratio in the melt x i The relationship is given by phase equilibrium theory: in: , These are the activity coefficients of Ag and Bi in the melt, respectively; , y represents the vapor pressures (in Pa) of pure Ag and pure Bi at evaporation temperature T, respectively, given by the Clausius-Clapeyron equation. i This refers to the Ag / Bi molar ratio in the steam produced by the i-th evaporation plate. i The molar ratio of Ag / Bi in the melt in the i-th evaporation pan is given.

[0031] The goal of the calculation is to solve for a series of temperature values ​​T. i (where i is the evaporator layer number, from top to bottom i=1 to n), such that when the i-th evaporator layer is at temperature T i When operating below, the Ag / Bi molar ratio in the steam it produces is y i It is exactly equal to y0. This calculation yields a strictly decreasing temperature sequence from top to bottom, i.e., T1>T2>…>T n This temperature gradient is the basis for achieving a high temperature in the upper layer to promote rapid bismuth evaporation and a low temperature in the lower layer to suppress excessive silver volatilization.

[0032] Preferably, in step S1, the target temperature T i It is determined by satisfying the following equations derived from phase equilibrium theory: y0 Where: y0 is the target value of Ag / Bi molar ratio in distilled bismuth, x i γ is the molar ratio of Ag / Bi in the melt in the i-th evaporation pan. Ag and γ Bi Activity coefficients of Ag and Bi, ΔS Ag-vap and ΔS Bi-vap Molar evaporation entropy of Ag and Bi, ΔH Ag-vap and ΔH Bi-vap Let be the molar enthalpy of vaporization of Ag and Bi, respectively, and R be the ideal gas constant.

[0033] S2. Establish the functional relationship between the cross-sectional area and height of the graphite heating element.

[0034] The purpose of this step is to convert the "temperature requirement" calculated in the previous step into the "geometry" of the heating element itself.

[0035] Specifically: The heating element transfers heat to the evaporation plate through thermal radiation, and its local radiation power depends on the temperature and surface area at that location; while the local temperature and resistance of the heating element are determined by its geometric dimensions (cross-sectional area) and material properties.

[0036] Based on the discrete temperature point T obtained in step S1 i and its corresponding height position h i (Taking the center of the lowest evaporator as the zero point of height), derive the following by combining the following laws: In a vacuum environment, the graphite heating element transfers heat to the evaporation plate through thermal radiation. This is based on the Stefan-Boltzmann radiation law. In industrial practice, the evaporator temperature T and the power Q of the graphite electrode heating element have an approximately linear relationship: Q i =CT' i 4 in: Q i The thermal radiation power of the graphite heating element at the height of the i-th evaporation disk (unit: W); ε is the emissivity of the graphite heating element (dimensionless, taken as 0.85). σ is the Stefan-Boltzmann constant (a constant, σ = 5.67 × 10⁻⁶). -8 W / (m 2 K 4 )); A represents the radiating area of ​​the graphite heating element at the corresponding height (unit: m²). 2 Here, we take a ring with an outer diameter of 10cm; C is a constant, C=k k is a correction factor, with a value ranging from 0.85 to 0.95; T i Let T' be the temperature of the evaporator plate in the i-th layer. i Let T' be the temperature of the graphite heating element corresponding to the evaporation disk of the i-th layer. i =T i (Unit: K); The sum of the power of all graphite heating elements .

[0037] Further calculations were performed to determine the relationship between the resistance of the graphite heating element and temperature and cross-sectional area.

[0038] The resistance of the heating element in the section corresponding to the height of the i-th evaporation disk follows the law of resistance: According to Joule's law, the electrothermal power Q generated by the heating element in the i-th segment... i : Q i =I 2 R i In the formula: I represents the constant operating current passing through the entire heating element; R i The resistance of the heating element in the section corresponding to the height of the i-th evaporator plate (unit: Ω); L is the length of the heating element unit corresponding to the distance between adjacent evaporation plates (unit: m; in the specific embodiment, L = 0.03 m is taken to match the height of the evaporation plate). T i Let T' be the temperature of the evaporator plate in the i-th layer. i Let T' be the temperature of the graphite heating element corresponding to the evaporation disk of the i-th layer. i =T i (Unit: K); S i Cross-sectional area of ​​the heating element (unit: m²) 2 ).

[0039] ρ0 is the resistivity of graphite at a reference temperature T'0 (usually taken as 298K) (taken as 2.0 × 10⁻⁶). -5 Ω m); α is the temperature coefficient of resistance of graphite (taken as 2.5 × 10⁻⁶). -4 K -1 ); In a specific embodiment, the relationship between the cross-sectional area and height h of the graphite heating element is further calculated. In step S2, the specific derivation of the functional relationship S=f(h) is based on the following formula: S(h) Where, let K = The formula then becomes In a specific embodiment, C is a constant. =k k is 0.9; T' i =T i =1.027T i , (unit: K).

[0040] In a specific embodiment, in step S2, by solving a simultaneous equation and eliminating intermediate variables, the cross-sectional area S of the graphite heating element is directly derived. i Its height h i The correspondence is obtained, that is, a set of discrete (S) i h i The design point is then determined. Furthermore, through mathematical fitting, a continuous and smooth functional relationship S=f(h) can be obtained. This function explicitly specifies the cross-sectional area of ​​the heating element required to generate thermal radiation power at a height h that exactly matches the target temperature T(h) at a given constant operating current I. The functional form used for fitting includes, but is not limited to, quadratic polynomials, piecewise linear functions, or exponential functions.

[0041] In a specific embodiment, the functional relationship S=f(h) can be specified as a quadratic polynomial in height h: S(h)=a-bh-ch 2 Where a, b, and c are constants determined through derivation and fitting based on specific process parameters and physical property data. The quadratic function form ensures accuracy while facilitating engineering description and processing.

[0042] S3. Manufacturing variable cross-section graphite heating elements.

[0043] Based on the functional relationship S=f(h) determined in step S2, high-density graphite material is machined into a solid heating element with a continuously varying or segmented stepped cross-sectional area along its height direction. The shape of the finished heating element is the physical realization of the designed function.

[0044] Secondly, the present invention provides a bismuth refining vacuum furnace that applies the above-described design method.

[0045] The vacuum furnace includes a furnace body, n annular evaporation plates arranged within the furnace body, a graphite heating element vertically inserted at the center of each evaporation plate, and a condensation collection system. The cross-sectional area of ​​the graphite heating element is not constant, but varies continuously or piecewise along its height according to a specific functional law S=f(h). This functional law is determined by the aforementioned design method, ensuring that the heating element can spontaneously form a temperature gradient field optimally matched to the changes in material composition when a rated current is applied.

[0046] Preferably, the cross-sectional area S of the graphite heating element decreases with increasing height h. More preferably, its variation follows a quadratic function relationship: S(h) = a - bh - ch 2 .

[0047] In a specific embodiment, the number of evaporation disk layers n is 30 to 40 layers.

[0048] In a specific embodiment, the graphite heating element is made of high-density isostatically pressed graphite.

[0049] To facilitate understanding of the present invention, the present invention will be described more fully and in detail below with reference to preferred embodiments, but the scope of protection of the present invention is not limited to the following specific embodiments.

[0050] Unless otherwise defined, all technical terms used herein have the same meaning as commonly understood by those skilled in the art. The technical terms used herein are for the purpose of describing particular embodiments only and are not intended to limit the scope of the invention.

[0051] Unless otherwise specified, all raw materials, reagents, instruments and equipment used in this invention can be purchased from the market or prepared by existing methods.

[0052] Example 1 This embodiment aims to process crude bismuth raw material containing 5000g / t of silver to produce distilled bismuth with a silver content of ≤30g / t (national standard 1#Bi requires ≤40g / t). A graphite heating element for a vacuum refining furnace with 35 layers (n=35) of annular evaporation plates is designed.

[0053] (a) Design conditions and basic parameter settings Process objectives: Raw material processing capacity: approximately 916.67 kg / h; Raw material composition: Bi≈95%, Ag=5000g / t; Target Ag content in distilled bismuth: ≤30g / t; Bi content in the residue: approximately 88.9%.

[0054] Molar ratio conversion: The initial molar ratio of Ag / Bi in the raw material is x0 ≈ 1.01 × 10⁻⁶ 2 ; The target Ag / Bi molar ratio in distilled bismuth is y0≈5.81×10⁻⁶. 5 ; Final molar ratio of Ag / Bi in residue x 35 ≈2.36×10 2 .

[0055] Material properties: Bi: Molar enthalpy of vaporization ΔH Bi =128kJ / mol, molar entropy of evaporation ΔS Bi =46.8 J / (mol) K), activity coefficient γ Bi ≈1.03; Ag: Molar enthalpy of vaporization ΔH Ag =255.1 kJ / mol, molar entropy of evaporation ΔS Ag =82.5 J / (mol) K), activity coefficient γ Ag Take 2.8; The ideal gas constant R = 8.314 J / (mol) K).

[0056] Graphite heating element material parameters: Material: High-density isostatic graphite At room temperature (298K), the resistivity ρ0 = 2.0 × 10⁻⁶ 5 Ω m; Temperature coefficient of resistance α = 2.5 × 10 4 K 1 Surface emissivity ε=0.85 k=0.9.

[0057] Electrothermal and structural parameters: The design operating current is I = 3600A, and the distance between adjacent evaporator plates (corresponding to the length of the heating element unit) is L = 0.03m.

[0058] (II) Design Steps Step S1: Calculate the target temperature gradient for each evaporation plate.

[0059] To achieve the desired Ag / Bi molar ratio in the steam generated by each evaporation plate iThe process objective of "all values ​​equal to the target value y0" is calculated iteratively by substituting the above parameters into the Clausius-Clapeyron equation and the vacuum distillation phase equilibrium theory.

[0060] Calculations yielded the target temperature T required for the 35 evaporation layers from top to bottom. i (K) and its corresponding Celsius temperature. Calculation results show that the temperature continuously decreases from the upper layer to the lower layer, as shown in Table 1. A gradient distribution is formed from top to bottom, with the temperature gradually decreasing from approximately 1186.5℃ to approximately 1067.1℃. Simultaneously, the Ag / Bi molar ratio x of the melt in each evaporation pan... i As the material flow gradually increases from the initial x0 to the final x 35 .

[0061] Step S2: Derive the functional relationship between the cross-sectional area and height of the graphite heating element.

[0062] To achieve the temperature gradient calculated in step S1, the thermal radiation power emitted by the graphite heating element at each height position when a constant current I is applied needs to match the required temperature of the corresponding evaporation plate. This is derived by combining Joule's law, the law of resistance, and the Stefan-Boltzmann radiation law.

[0063] The layers T obtained in step S1 i By substituting the known parameters into the simultaneous formulas of Joule's law, the law of resistance, and the law of radiation, a set of discrete theoretical cross-sectional area design values ​​Si corresponding to the height hi of each floor can be calculated. The data is shown in Table 2. The calculated discrete data points (h...) i S i Mathematical fitting is performed to obtain a continuous, manufacturable geometric shape function S=f(h).

[0064] In this embodiment, a quadratic polynomial was used for fitting, which resulted in an extremely high goodness of fit.

[0065] The quadratic function obtained by fitting is: S(h)=0.003902-0.000769h-0.000256h 2 (Unit: m) 2 (0≤h≤1.02m) Where h is the height with the center of the lowest evaporation disk as the origin. This function shows that the cross-sectional area S of the graphite heating element decreases with increasing height h, meaning the heating element has a variable cross-sectional shape that is thicker at the top and thinner at the bottom. Calculations show that the goodness of fit of this function is close to 100%, with extremely small residuals (≤ ±7.3 × 10⁻⁶). -6 m 2 ),like Figure 1 As shown.

[0066] Step S3: Manufacturing the graphite heating element Based on the functional relationship S(h) determined in step S2, high-density isostatically pressed graphite rods are precision machined using CNC machine tools to manufacture a graphite heating element with a continuously varying cross-sectional area along the height direction. During the machining process, the cross-sectional dimensional error is strictly controlled within ±0.01×10⁻⁶. -3 m 2 Within this range, to ensure that the actual heat generation power distribution is consistent with the design target.

[0067] (III) Implementation Results The fabricated variable cross-section graphite heating element was installed in a 35-layer evaporation plate vacuum furnace for industrial-scale testing. A comparison was made with a traditional vacuum furnace using a constant cross-section cylindrical graphite heating element under the same raw materials and similar production capacity conditions. The results are as follows: Product purity: The vacuum furnace using the heating element of this invention produces distilled bismuth with a stable silver content of 21.8~26.5 g / t, consistently below the target value of 30 g / t, and with minimal fluctuation. In contrast, the silver content of products from conventional constant-section furnaces often approaches or exceeds 30 g / t, exhibiting significant fluctuations.

[0068] Production capacity: Due to the precise matching of heat, the design of this invention can achieve a bismuth distillation production capacity of 505.1~526.7 kg / h under the same power, which is a significant improvement over the production capacity (approximately 436 kg / h) sacrificed by traditional equal cross-section furnaces to maintain purity.

[0069] Table 1: Calculation Table of Target Temperature of Evaporator Pan and Melt Composition Table 2: Design Values ​​of Heating Element Cross-sectional Area and Fitting Residuals Example 2: Design of a Variable Cross-Section Graphite Heating Element Based on Piecewise Linear Approximation This embodiment aims to illustrate the process of obtaining discrete design points (h). i S i After that, in addition to fitting continuous functions, piecewise linear functions can also be used for approximate design to simplify the process.

[0070] Design Basis: The same process objectives, raw materials (containing 5000 g / t of silver), and furnace structure (35-layer evaporation trays) as in Example 1 are adopted. The target temperature gradient T calculated in step S1... i and the discrete cross-sectional area design point (h) initially derived in step S2 i S i It is exactly the same as Example 1.

[0071] Step S2 (Fitting Method Change): To facilitate manufacturing, the heating element with a total height H = 1.02m is divided into several segments (e.g., 3 or 5 segments). Within each segment, a straight line is used to approximate the trend of cross-sectional area variation. By selecting appropriate breakpoints and using the least squares method to linearly fit the discrete points within each segment, a set of piecewise linear functions can be obtained to describe S(h).

[0072] For example, dividing the height range into three segments (0~0.34m, 0.34~0.68m, 0.68~1.02m) and performing linear fitting on each segment yields a function of the following form: When 0 ≤ h < 0.34, S(h) = a1 b1h When 0.34 ≤ h < 0.68, S(h) = a2 b2h When 0.68 ≤ h ≤ 1.02, S(h) = a3 b3h Where a1, b1, a2, b2, a3, and b3 are constants determined by fitting specific discrete points. This design essentially approximates a continuous variable cross-section as a combination of several segments of truncated cones with different tapers. Although it is not strictly continuous and smooth, as long as the segmentation is reasonable, the heat power distribution it provides can still basically meet the temperature gradient requirements, and the processing difficulty is reduced.

[0073] Step S3: Based on the dimensions determined by the piecewise linear function, process the graphite heating element in segments, and then assemble or process it as a whole into a stepped, approximately continuously changing shape.

[0074] Effects: The heating element manufactured using this piecewise linear design can also achieve a gradient distribution with high temperature in the upper layer and low temperature in the lower layer, effectively controlling the bismuth silver content in distillation. It is superior to the traditional constant cross-section design in terms of energy consumption and production capacity, demonstrating the flexibility of the design method of this invention in terms of implementation.

[0075] Example 3: Application of design methods adapted to different silver contents in raw materials This embodiment illustrates how to apply the design method of the present invention to adjust the process when the silver content of the raw material changes, so as to reflect its process adaptability.

[0076] Design conditions changed: Assume the silver content of the raw material becomes 2000g / t (corresponding to molar ratio x0'), but the target purity of distilled bismuth, furnace structure (35-layer evaporation plate), and basic parameters of graphite and electrothermal remain unchanged.

[0077] Design steps: Step S1 (Recalculate the temperature gradient): Set the new initial molar ratio x0', target molar ratio y0, and final molar ratio of the residue x... n(This needs to be re-determined based on material balance) Substitute the same phase equilibrium equation into the equation and perform iterative calculations to obtain a new target temperature sequence T suitable for low-silver raw materials. i Typically, due to the reduced initial silver content, the required temperatures for each layer to achieve the same separation effect may differ from those in Example 1.

[0078] Step S2 (Re-derive the cross-sectional area function): The new temperature sequence T... i Substituting into the same derivation formula, a new set of discrete design points (h) is calculated. i S i Then, a quadratic function, piecewise linear function, or other functional form can be selected for fitting to obtain a new functional relationship S'(h) = f'(h). The shape of this function (such as the rate of decrease) will be different from S(h) in Example 1, reflecting the adjustment of heat distribution due to changes in material composition.

[0079] Step S3 (Processing and Manufacturing): Process the graphite heating element according to the new function S'(h).

[0080] Results: Through the above redesign, even if the silver content of the raw material decreases from 5000g / t to 2000g / t, a matching variable cross-section graphite heating element can still be designed to ensure the production of qualified distilled bismuth under optimal energy consumption. This verifies that the design method of this invention can flexibly adapt to fluctuations in raw material composition. It only requires re-execution of the design process according to the new process parameters, without changing the core mechanical structure of the vacuum furnace, and has strong process adaptability.

[0081] The above embodiments are merely several specific implementations of the present invention. Those skilled in the art will understand that various modifications and alternatives can be made without departing from the core principles of the present invention.

[0082] The specific mathematical form of the cross-sectional area function S=f(h) is not limited to a quadratic polynomial or a piecewise linear function. Depending on the distribution characteristics of discrete design points and engineering requirements, exponential functions, higher-order polynomials, spline functions, etc., can also be used for high-precision fitting.

[0083] The core design concept of this invention, "based on the dynamic changes in material composition (the proportion of components with high volatility) during multi-stage evaporation, determining the required temperature gradient through thermodynamic calculations, and designing the variable cross-sectional geometry of the heating element accordingly to achieve this gradient," can be extended to other vacuum metallurgical processes with similar separation requirements. For example, when processing other two-component or multi-component alloys with significant differences in volatility, such as bismuth-lead and zinc-silver alloys, it is only necessary to adjust the relevant physical property parameters (ΔH) in the formula. vap ΔS vap By replacing the parameters (e.g., γ, etc.) with the corresponding components, the graphite heating element can be customized using the same method.

[0084] The graphite heating element can be a solid object with a smooth and continuously varying cross-section, or it can be a stepped structure composed of multiple columns with different constant cross-sections, which macroscopically approximates the law of cross-sectional area variation. As long as the overall heat power distribution it provides can basically conform to the trend described by the function S=f(h), it should be considered to fall within the protection concept of this invention.

[0085] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method for designing a graphite heating element for a bismuth refining vacuum furnace, wherein the vacuum furnace has n layers of annular evaporation disks stacked from top to bottom, and a graphite heating element is vertically inserted through the center of each evaporation disk layer, characterized in that... The design method includes the following steps: S1. Determine the target temperature T for each evaporator layer. i Based on the initial molar ratio of silver to bismuth in the raw material melt x0, the target molar ratio of silver to bismuth in the distilled bismuth y0, and the final molar ratio of silver to bismuth in the residue x n Combining the Clausius-Clapeyron equation, the phase equilibrium theory of vacuum distillation, and Raoult's law, the molar ratio y of silver to bismuth in the vapor produced by each evaporation pan was calculated. i When all values ​​are equal to y0, the required temperature T for each evaporation plate is... i Where i is the evaporator disk layer number, from top to bottom i=1 to n, and T1>T2>…>T n ; S2. Establish the functional relationship between the cross-sectional area S of the graphite heating element and its height h: based on the discrete temperature point T obtained in step S1. i and the corresponding evaporator center height h i By combining Joule's law, the law of resistance, and the Stefan-Boltzmann radiation law, a continuous functional relationship S=f(h) is obtained for the cross-sectional area S of the graphite heating element along its height h, where the height h is taken as the reference zero point at the center of the lowest evaporation disk. The function f(h) satisfies that when a constant working current I is applied to the entire graphite heating element, the local thermal radiation power of the heating element at height h matches the target temperature T(h) required by the evaporation disk at the corresponding height. S3. Manufacturing a graphite heating element: Based on the functional relationship S=f(h) obtained in step S2, manufacture a graphite heating element whose cross-sectional area varies continuously or segmentally along its height direction.

2. The design method according to claim 1, characterized in that, In step S1, the target temperature T i Determined by the following formula: y0 Where y0 is the target value of the Ag / Bi molar ratio in distilled bismuth, and x i γ is the molar ratio of Ag / Bi in the melt in the i-th evaporation pan. Ag and γ Bi Activity coefficients of Ag and Bi, ΔS Ag-vap and ΔS Bi-vap Molar evaporation entropy of Ag and Bi, ΔH Ag-vap and ΔH Bi-vap Here are the molar enthalpy of vaporization for Ag and Bi, respectively, and R is the ideal gas constant with a value of 8.314 J / (mol·K).

3. The design method according to claim 1, characterized in that, In step S2, the cross-sectional area S of the graphite heating element at the height of the i-th evaporation disk is... i Determined by the following formula: Where I is the design operating current, ρ0 is the resistivity of the graphite material at the reference temperature T'0, and T ' 0 represents the reference temperature for graphite resistivity (298 K), L represents the length of the heating element unit corresponding to the distance between adjacent evaporation disks, α represents the temperature coefficient of resistance of the graphite material, and T represents the temperature coefficient of resistance of the graphite material. i Let T be the temperature of the evaporator plate in the i-th layer. ' i The temperature of the graphite heating element corresponding to the evaporation disk of the i-th layer; C=k ε is the emissivity of the graphite heating element, σ is the Stefan-Boltzmann constant, A is the radiating area of ​​the graphite heating element at the corresponding height, and k is a correction factor with a value ranging from 0.85 to 0.95; T' i =T i .

4. The design method according to claim 1, characterized in that, In step S2, the calculated discrete data points (S) are processed. i h i The continuous function relationship S=f(h) is obtained by mathematical fitting. The function form used for fitting includes, but is not limited to, quadratic polynomial, piecewise linear function or exponential function.

5. The design method according to claim 4, characterized in that, The functional relationship S=f(h) obtained in step S2 is a quadratic function: S(h)=a-bh-ch 2 Where a, b, and c are constants determined based on specific process parameters, physical property parameters, and electrothermal parameters, 0 ≤ h ≤ H, and H is the height corresponding to the uppermost evaporation plate.

6. The design method according to any one of claims 1 to 5, characterized in that, The functional relationship S=f(h) satisfies that the cross-sectional area S of the graphite heating element decreases as the height h increases.

7. A bismuth refining vacuum furnace, comprising a furnace body, n layers of annular evaporation plates disposed within the furnace body, a graphite heating element vertically disposed at the center of each evaporation plate, and a condensation collection system, characterized in that, The cross-sectional area of ​​the graphite heating element varies continuously or segmentally along its height direction, and its variation follows the functional relationship S=f(h) determined by the design method described in any one of claims 1 to 6.

8. The bismuth refining vacuum furnace according to claim 7, characterized in that, The cross-sectional area S of the graphite heating element decreases with increasing height h.

9. The bismuth refining vacuum furnace according to claim 7, characterized in that, The number n is 30 to 40 layers.

10. The bismuth refining vacuum furnace according to claim 7, characterized in that, The graphite heating element is made of high-density isostatically pressed graphite.

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