Thermodynamic model of the hydration reaction of hemihydrate phosphogypsum based on the temperature effect
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摘要: 為擴大半水磷石膏（HPG）作為充填膠凝材料的工業應用半徑，實現HPG資源化利用技術新突破。本文尋求一種在堆存過程中HPG水化反應放熱量變化的模型，以了解其膠凝性能的變化情況。通過對初始溫度為35、40、60和80 ℃的HPG堆體進行自由水質量分數和溫度監測，發現HPG自由水質量分數變化規律符合一級反應動力學模型，之后基于熱力學和化學反應動力學基本理論，提出了一種關于堆存溫度與時間關系的HPG水化反應熱動力學模型。最后，采用COMSOL Multiphysics數值模擬軟件，將HPG水化反應熱動力學方程嵌入傳熱和ODE模塊，對HPG堆體溫度進行數值模擬，模擬堆體溫度變化曲線與試驗結果較為吻合，驗證了所提出模型的可靠性。Abstract: Hemihydrate phosphogypsum (HPG), as a cementing material for mine filling, will spontaneously transform into phosphogypsum (PG) in the stockpiling state. The gelling activity decreases, and meeting the requirements of mechanical properties required for long-distance mine filling becomes difficult. The key measure in expanding the industrial application radius of HPG as a filling cementitious material is the prevention of the spontaneous conversion of HPG to PG. In-depth research on the conversion process of HPG in the storage state is required to achieve a breakthrough in the HPG resource utilization technology. In the storage process, the HPG chemical reaction will release the heat of hydration, causing the temperature and chemical fields in the system to interact with each other and promote the conversion of HPG to PG. Therefore, the HPG hydration heat release process is accurately calculated, analyzed, and simulated. This is a prerequisite to effectively inhibit the conversion of HPG. This article seeks a model of the heat release of the HPG hydration reaction during the storage process to understand the change of its gelation performance and guide on-site industrial applications. The monitoring of the free water mass fraction and the temperature of HPG stacks with initial temperatures of 35 °C, 40 °C, 60 °C, and 80 °C reveals that the HPG free water mass fraction change law conforms to the first-order reaction kinetic model. Based on thermodynamics and chemical reaction kinetics, a thermal kinetic model of the HPG hydration reaction on the relationship between the storage temperature and time is proposed. Using the COMSOL Multiphysics numerical simulation software, the HPG hydration reaction thermokinetic equation was then embedded in the heat transfer and ODE modules, and the HPG reactor temperature was numerically simulated. The simulated reactor temperature curve was more consistent with experimental results, and the reliability of the proposed model was verified. This model can provide guidance for the later design of the delaying HPG conversion plan and has very important practical significance for the promotion and application of HPG.
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圖 2 堆體內部溫度與化學相互耦合作用關系圖
Figure 2. Relationship between the temperature and chemical interaction in the reactor
圖 4 不同初始堆存溫度下自由水質量分數回歸擬合.（a）35 ℃；（b）40 ℃；（c）60 ℃；（d）80 ℃
Figure 4. Regression fit of the free water mass fraction at different initial storage temperatures: (a) 35 ℃; (b) 40 ℃; (c) 60 ℃; (d) 80 ℃
圖 5 反應速率常數隨初始堆存溫度的變化趨勢
Figure 5. Trends of reaction rate constants with the initial storage temperature
圖 7 本構模型嵌入. (a) 傳熱模塊設置；(b) ODE模塊設置
Figure 7. Constitutive model embedding: (a) heat transfer module setup; (b) ODE module setup
圖 8 模擬溫度變化曲線與試驗結果對比. (a) 內部溫度；(b) 表面溫度
Figure 8. Comparison of the simulated temperature change curve with the test results: (a) internal temperature; (b) surface temperature
圖 9 不同初始堆存溫度HPG堆體堆存36 h后溫度云圖. (a) 35 ℃；(b) 40 ℃；(c) 60 ℃；(d) 80 ℃
Figure 9. Temperature cloud diagram after storage of 36 h HPG with different initial storage temperatures: (a) 35 ℃; (b) 40 ℃; (c) 60 ℃; (d) 80 ℃
表 1 HPG相關性質參數
Table 1. Property parameters of HPG
Material Free water mass fraction/% Crystal water mass
fraction /%Porosity/% HPG 22.10 5.40 52.95 
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表 2 相關物質熱力學數據
Table 2. Thermodynamic data for related substances
Compounds Standard Gibbs free energy, $\Delta G_T^{\ominus }$/(kJ·mol?1) Standard molar enthalpy of formation, $\Delta H_T^{\ominus }$/(kJ·mol?1) CaSO4·2H2O(s) ?2080.51 ?2022.63 CaSO4·0.5H2O(s) ?1615.66 ?1576.74 H2O(aq) ?306.68 ?285.83
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表 3 不同初始堆存溫度條件下HPG自由水質量分數變化規律數學擬合結果
Table 3. Mathematical fitting results of the variation law of the HPG free water mass fraction under different initial storage temperatures
Initial storage temperature/℃ Fitting equation Reaction rate constant ,k R2 35 $ Z = 18.79 \times {{\text{e}}^{ - 0.1903}}^t $ 0.1903 0.9626 40 $ Z = 15.81 \times {{\text{e}}^{ - 0.2152}}^t $ 0.2152 0.9270 60 $ Z = 12.30 \times {{\text{e}}^{ - 0.3773}}^t $ 0.3773 0.9261 80 $ Z = 10.26 \times {{\text{e}}^{ - 0.4938}}^t $ 0.4938 0.8865
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中文字幕在线观看表 4 相關參數設置
Table 4. Relevant parameter settings
Parameters Value Activation energy, Ea / (J·mol?1) 15300 Frequency factor, A / s?1 87.99 Convection heat transfer coefficient, Uk / (W·m?2·K?1) 20 Thermal conductivity, TC / (W·m?1·K?1) 0.33 HPG density, HD / (kg·m?3) 1500 Reaction heat, RH / (kJ·kg?1) 118.28 Thermal capacity, Cp / (J·kg?1·K?1) 1050 Initial storage temperature, T0 / K 308.15, 313.15,
333.15, 353.15Pore media Air
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