Thermodynamic model of the hydration reaction of hemihydrate phosphogypsum based on the temperature effect
-
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.
-
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 
下載: 導出CSV
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
下載: 導出CSV
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
下載: 導出CSV
久色视频表 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
下載: 導出CSV
-
參考文獻
[1] Yang L, Cao J X, Liu Y M. Mineralogical characteristics of hemi-hydrate phosphogypsum. Acta Petrol et Mineral, 2015, 34(6): 827 doi: 10.3969/j.issn.1000-6524.2015.06.005楊林, 曹建新, 劉亞明. 半水磷石膏的礦物學特征. 巖石礦物學雜志, 2015, 34(6):827 doi: 10.3969/j.issn.1000-6524.2015.06.005 [2] Wang Y M, Wang Z K, Wu A X, et al. Preparation of new cementitious backfilling material and its curing mechanism analysis. Met Mine, 2018(6): 20王貽明, 王志凱, 吳愛祥, 等. 新型膠凝充填材料制備及固化機理分析. 金屬礦山, 2018(6):20 [3] Lan W T, Wu A X, Wang Y M, et al. Experimental study on influencing factors of the filling strength of hemihydrate phosphogypsum. J Harbin Inst Technol, 2019, 51(8): 128 doi: 10.11918/j.issn.0367-6234.201804082蘭文濤, 吳愛祥, 王貽明, 等. 半水磷石膏充填強度影響因素試驗. 哈爾濱工業大學學報, 2019, 51(8):128 doi: 10.11918/j.issn.0367-6234.201804082 [4] Yan P Y, Zheng F. Kinetics model for the hydration mechanism of cementitious materials. J Chin Ceram Soc, 2006, 34(5): 555 doi: 10.3321/j.issn:0454-5648.2006.05.009閻培渝, 鄭峰. 水泥基材料的水化動力學模型. 硅酸鹽學報, 2006, 34(5):555 doi: 10.3321/j.issn:0454-5648.2006.05.009 [5] Li L X, Xie Y J, Feng Z W, et al. Cement hydration mechanism and research methods. Concrete, 2011(6): 76李林香, 謝永江, 馮仲偉, 等. 水泥水化機理及其研究方法. 混凝土, 2011(6):76 [6] Han F H, Liu J H, Yan P Y. Effect of temperature on hydration of composite binder containing slag. J Chin Ceram Soc, 2016, 44(8): 1071韓方暉, 劉娟紅, 閻培渝. 溫度對水泥-礦渣復合膠凝材料水化的影響. 硅酸鹽學報, 2016, 44(8):1071 [7] Lü Q H, Xiao L Z. Temperature effect of cement-based materials based on hydration kinetics model. J Wuhan Inst Technol, 2020, 42(4): 434呂全紅, 肖蓮珍. 基于水化動力學模型的水泥基材料溫度效應. 武漢工程大學學報, 2020, 42(4):434 [8] Ulm F J, Coussy O. Modeling of thermochemomechanical couplings of concrete at early ages. J Eng Mech, 1995, 121(7): 785 doi: 10.1061/(ASCE)0733-9399(1995)121:7(785) [9] Suzuki M, Fukuura N, Takeda H, et al. Establishment of coupled analysis of interaction between structural deterioration and reinforcement corrosion by salt damage. J Adv Concr Technol, 2016, 14(9): 559 doi: 10.3151/jact.14.559 [10] Gawin D, Pesavento F, Schrefler B A. Hygro-thermo-chemo-mechanical modelling of concrete at early ages and beyond. Part I: Hydration and hygro-thermal phenomena. Int J Numer Meth Engng, 2006, 67(3): 299 [11] Feng C Q, Yu X M, Chang X L, et al. The deduction and application of a hydration model for concrete based on chemical reaction kinetics. China Rural Water Hydropower, 2019(1): 152 doi: 10.3969/j.issn.1007-2284.2019.01.029馮楚橋, 余曉敏, 常曉林, 等. 混凝土水化化學反應動力學模型的推導及應用. 中國農村水利水電, 2019(1):152 doi: 10.3969/j.issn.1007-2284.2019.01.029 [12] Liu S H, Wang L, Gao Y X, et al. Influence of fineness on hydration kinetics of supersulfated cement. Thermochimica Acta, 2015, 605: 37 doi: 10.1016/j.tca.2015.02.013 [13] Neusinger R, Drach V, Ebert H P, et al. Computer simulations that illustrate the heat balance of landfills. Int J Thermophys, 2005, 26(2): 519 doi: 10.1007/s10765-005-4513-x [14] Wang Z K, Wang Y M, Wu A X, et al. Effect of storage temperature on the cementitious property of hemihydrate phosphogypsum. Chin J Eng, 2022, 44(5): 840王志凱, 王貽明, 吳愛祥, 等. 堆存溫度對半水磷石膏膠凝性能影響. 工程科學學報, 2022, 44(5):840 [15] Liu X H, Zhang C, Chang X L, et al. Precise simulation analysis of the thermal field in mass concrete with a pipe water cooling system. Appl Therm Eng, 2015, 78: 449 doi: 10.1016/j.applthermaleng.2014.12.050 [16] Yang X W, He A P, Yuan B C. Manual for the Calculation of Thermodynamic Data in High Temperature. Beijing: Metallurgical Industry Press, 1983楊顯萬, 何藹平, 袁寶州. 高溫水溶液熱力學數據計算手冊. 北京: 冶金工業出版社, 1983 [17] Li X B. Crystal Morphology Control and Hydration Hardening Properties of High Strength Α-Hemihydrate Phosphogypsum [Dissertation]. Guiyang: Guizhou University, 2019李顯波. 高強α半水磷石膏晶形調控及水化硬化性能研究[學位論文]. 貴陽: 貴州大學, 2019 [18] Hong Q Y. Study on influence factors of rate of chemical reaction. Guangzhou Chem Ind, 2017, 45(17): 201 doi: 10.3969/j.issn.1001-9677.2017.17.072洪清揚. 探析影響化學反應速率的因素. 廣州化工, 2017, 45(17):201 doi: 10.3969/j.issn.1001-9677.2017.17.072 [19] Zheng X, Chen Z B. Exploration into temperature-chemical coupling effect in landfill disposal of household rubbish in urban area. J Kunming Univ, 2015, 37(3): 77鄭旴, 陳澤斌. 城市生活垃圾填埋處置中的溫度-化學耦合作用探討. 昆明學院學報, 2015, 37(3):77 [20] Yang J. A Study of Coupled Temperature and Chemical Processes in Municiple Solid Waste’s Landfill [Dissertation]. Chengdu: Southwest Jiaotong University, 2007楊軍. 城市生活垃圾填埋處置中的溫度-化學耦合作用研究[學位論文]. 成都: 西南交通大學, 2007 [21] Xiao Y F, Li W B. Physical Chemistry. 2nd Ed. Tianjin: Tianjin University Press, 2004肖衍繁, 李文斌. 物理化學. 2版. 天津: 天津大學出版社, 2004 [22] Zhao X Z. Principle of Chemical Reaction Dynamics. Beijing: Higher Education Press, 1984趙學莊. 化學反應動力學原理. 北京: 高等教育出版社, 1984 [23] Zhang Z X, Guo F, Song W, et al. Empirical correction of kinetic model for polymer thermal reaction process based on first order reaction kinetics. Chin J Chem Eng, 2021, 38: 132 doi: 10.1016/j.cjche.2020.09.023 [24] Reddy M G, Naveen Kumar R, Prasannakumara B C, et al. Magnetohydrodynamic flow and heat transfer of a hybrid nanofluid over a rotating disk by considering Arrhenius energy. Commun Theor Phys, 2021, 73(4): 045002 doi: 10.1088/1572-9494/abdaa5 [25] Yang L. Evolution of Mineralogical Characteristics and Gelling Properties of Hemi-Hydrate Phosphogypsum [Dissertation]. Guiyang: Guizhou University, 2016楊林. 半水磷石膏礦物學特征及膠凝性能變化行為[學位論文]. 貴陽: 貴州大學, 2016 [26] Wang Y, Wu A X, Wang H J, et al. Damage constitutive model of cemented tailing paste under initial temperature effect. Chin J Eng, 2017, 39(1): 31王勇, 吳愛祥, 王洪江, 等. 初始溫度條件下全尾膠結膏體損傷本構模型. 工程科學學報, 2017, 39(1):31 -
點擊查看大圖
計量
- 文章訪問數: 531
- HTML全文瀏覽量: 221
- PDF下載量: 76
- 被引次數: 0
