基于熔渣結構的多元渣系黏度模型

唐續龍; 張梅; 郭敏; 王習東

doi:10.13374/j.issn2095-9389.2019.09.27.001

基于熔渣結構的多元渣系黏度模型

doi: 10.13374/j.issn2095-9389.2019.09.27.001

唐續龍¹,
張梅^2, ,,
郭敏²,
王習東³

1.
中國恩菲工程技術有限公司，北京 100038
2.
北京科技大學冶金與生態工程學院，北京 100083
3.
北京大學工學院，北京 100871

基金項目: 國家自然科學基金資助項目（51972019）；山西聯合重點基金資助項目（U1810205）

詳細信息

通訊作者:
E–mail：zhangmei@ustb.edu.cn

中圖分類號: TF02
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出版歷程
- 收稿日期: 2019-09-27
- 刊出日期: 2020-09-20

Structurally-based viscosity model for multicomponent slag systems

1.
China ENFI Engineering Corporation, Beijing 100038, China
2.
School of Metallurgical and Ecological Engineering, University of Science and Technology Beijing, Beijing 100083, China
3.
College of Engineering, Peking University, Beijing 100871, China

More Information

Corresponding author: E–mail: zhangmei@ustb.edu.cn

摘要

摘要: 黏度是冶金熔渣的基本物理性質，其大小直接影響到反應速率、熔渣分離效果等冶煉過程。通過深入探索熔渣黏度與其結構的關系，在分析熔渣黏度與其(NBO/T)比值（即單個聚合物粒子所擁有的非橋氧數量）相互關系的基礎上，本文提出基于（NBO/T）比值的多元熔渣黏度計算模型。首先建立SiO₂–∑M_xO簡單渣系的黏度計算模型，通過擬合純氧化物和SiO₂–M_xO二元渣系的黏度數據得到模型參數，擬合平均誤差在9%～18.5%之間；隨后將該模型擴展至SiO₂–Al₂O₃–∑M_xO多元渣系的黏度計算，針對Al₂O₃在熔渣中同時表現出酸性氧化物和堿性氧化物的特點，在計算SiO₂–Al₂O₃–M_xO三元渣系黏度時，將其中的Al₂O₃拆分為酸性物質和堿性物質來計算（NBO/T）比值和黏度活化能。在SiO₂–M_xO二元系模型參數的基礎上，通過擬合SiO₂–Al₂O₃–M_xO三元渣系的黏度數據得到含Al₂O₃渣系的模型參數，擬合平均誤差在10%～25%之間。利用該模型計算了SiO₂–Al₂O₃–CaO–MgO–FeO–Na₂O–K₂O–Li₂O–BaO–SrO–MnO多元復雜渣系及其子體系的黏度值，計算平均誤差在25%以內，取得了較好的預報效果。本模型基于熔渣結構理論，并借鑒了經驗模型的數據處理方式，在預報效果和適用范圍上都優于傳統經驗模型，在計算方式上比結構模型要簡單。
- 聚合度 /
- (NBO/T)比值 /
- 黏度模型 /
- 黏度 /
- 熔渣
Abstract: Viscosity is a physical property of fluids and shows resistance to flow. In metallurgical slag, it directly affects various parameters of a metallurgical process such as reaction rate, separation effect, etc. The estimation of viscosity by models during a production process is considered to be much more effective owing to the production fluctuations and complexities of the slag composition. Many viscosity models have been developed in the past, such as the structural model with a wide range of adaptability and complex calculation process and the empirical and semiempirical models with simple structure and a narrow range of adaptability. The present paper proposed a new method to calculate the structural parameter (NBO/T) ratio (the amount of nonbridging oxygen per tetrahedral-coordinated atom), based on which the relationship between the viscosity of molten slag and (NBO/T) ratio was investigated. First, the viscosity model was applied to SiO₂–ΣM_xO slags, with the model parameters obtained by fitting the viscosity data of pure oxide and SiO₂–M_xO binary slag, and the average deviations were in the range of 9%–18.5%. Then, the model was extended to calculate the viscosity of SiO₂–Al₂O₃–ΣM_xO, a multicomponent complex aluminosilicate system, and Al₂O₃ was split into acid and basic oxides. Then the oxides were used for calculating the (NBO/T) ratio and viscosity activation energy based on the amphoteric behavior of Al₂O₃ in SiO₂–Al₂O₃–M_xO ternary slag system. Using the parameters of a SiO₂–M_xO binary system, the model parameters of the Al₂O₃-containing slag system were obtained by fitting the viscosity data of the SiO₂–Al₂O₃–M_xO ternary slag system with average deviations between 10% and 25%. In addition, the viscosity of a multi-complex system (SiO₂–Al₂O₃–CaO–MgO–FeO–Na₂O–K₂O–Li₂O–BaO–SrO–MnO) and its subsystems were also calculated using the model proposed in this paper, and the average deviations is less than 25%, which shows relatively accurate prediction results. The present model is based on the analysis of a slag structure and processing of data by an empirical method. This method has a better prediction effect and wider application range compared with the traditional empirical model, and it uses a simpler calculation process compared with the structure model.
- degree of the polymerization /
- (NBO/T) ratio /
- viscosity model /
- viscosity /
- slag

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圖 1 SiO₂–M_xO二元系黏度與（NBO/T）比值的關系。（a） SiO₂–CaO^[9-11]；（b） SiO₂–MgO^[12]；（c） SiO₂–MnO^[10,13-14]；（d） SiO₂–FeO^[10,15-16]；（e） SiO₂–K₂O^[12-17]；（f） SiO₂–Na₂O^[11-12]

Figure 1. Relationship between the viscosity and (NBO/T) ratio of SiO₂–M_xO binary system: (a) SiO₂–CaO^[9-11]；(b) SiO₂–MgO^[12]；(c) SiO₂–MnO^[10,13-14]；(d) SiO₂–FeO^[10,15-16]；(e) SiO₂–K₂O^[12-17]；(f) SiO₂–Na₂O^[11-12]

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圖 2 SiO₂–M_xO二元系黏度活化能與（NBO/T）比值的關系。（a） SiO₂–CaO^[9-11]；（b） SiO₂–MgO^[9-10]；（c） SiO₂–MnO^[10,14]；（d） SiO₂–FeO^[16]；（e） SiO₂–K₂O^[12,17]；（f） SiO₂–Na₂O^[11,20]

Figure 2. Relationship between the viscosity activation energy and (NBO/T) ratio of SiO₂–M_xO binary system: (a) SiO₂–CaO^[9-11]；(b) SiO₂–MgO^[9-10]；(c) SiO₂–MnO^[10,14]；(d) SiO₂–FeO^[16]；(e) SiO₂–K₂O^[12,17]；(f) SiO₂–Na₂O^[11,20]

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圖 3 黏度模型的預報效果比較。（a） SiO₂–M_xO二元系；（b） SiO₂–Al₂O₃–M_xO三元系；（c） SiO₂–CaO/MgO–M_xO三元系；（c） SiO₂–Al₂O₃–∑M_xO復雜體系

Figure 3. Comparison of prediction effects of the viscosity model: (a) SiO₂–M_xO binaries slag; (b) SiO₂–Al₂O₃–M_xO ternary slag; (c) SiO₂–CaO/MgO–M_xO ternary slag; (c) SiO₂–Al₂O₃–∑M_xO multi–complex slag

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表 1 純M_xO熔渣的參數

Table 1. Parameters of pure M_xO slag

M_xO	μ/(mPa·s)				E_M_i/(kJ·mol^?1)	m_i
M_xO	1400 ℃	1450 ℃	1500 ℃	1530 ℃	E_M_i/(kJ·mol^?1)	m_i
CaO	23.82	20.67	17.83	16.15	10.703	0.582
MgO	39.66	34.01	28.96	26.03	11.458	0.526
K₂O	0.47	0.45	0.43	0.42	4.365	0.543
Na₂O	0.83	0.79	0.75	0.72	4.987	0.561
Li₂O	3.24	2.96	2.69	2.52	7.53	0.58
MnO	7.35	6.81	6.23	5.79	7.185	0.617
FeO	3.59	3.43	3.07	3.02	6.086	0.626
SrO^a)					20.329	0.568
BaO^a)					13.303	0.506
a)：The m of SrO and BaO are obtained by fitting the viscosities data of corresponding SiO₂-M_xO binary slag.

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表 2 SiO₂–M_xO二元渣系參數

Table 2. Parameters of SiO₂–M_xO binary slag

System	mass fraction of SiO₂/%	Temperature range/℃	K_i	q_i	Fitting errors/%
SiO₂–CaO^[9-11,22-24]	40–40	1500–2200	3.18	0.672	11.2
SiO₂–MgO^[10,12]	45–70	1600–2200	2.633	1.494	9.9
SiO₂–FeO^[15-16]	25–40	1250–1400	2.303	0.805	8.1
SiO₂–MnO^[13,22]	20–40	1450–1550	2.333	0.859	14.1
SiO₂–K₂O^[12,17]	40–80	1300–1700	2.556	0.272	18.5
SiO₂–Na₂O^[11-12,20]	40–85	1350–1700	2.901	0.247	11.5
SiO₂–Li₂O^[12,17]	60–80	1250–1700	4.229	0.683	9.3
SiO₂–SrO^[10,12,17]	35–70	1500–1800	19.156	2.016	10.0
SiO₂–BaO^[12,17]	25–70	1500–1800	6.403	0.943	16.6

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表 3 SiO₂–Al₂O₃–M_xO渣系參數

Table 3. Parameters of SiO₂–Al₂O₃–M_xO slag

System	$R_{{{\rm{M}}_x}{\rm{O1}}} $	$R_{{{\rm{M}}_x}{\rm{O2}}} $	$R_{{{\rm{M}}_x}{\rm{O}}} $	Fitting errors/%
SiO₂–Al₂O₃–Li₂O^[17]	3.92	?5.721	1.307	11.9
SiO₂–Al₂O₃–Na₂O^[20,26-27]	2.13	?0.954	10.904	24.4
SiO₂–Al₂O₃–K₂O^[17]	?3.666	14.831	?0.247	19.1
SiO₂–Al₂O₃–SrO^[17]	4.519	?8.03	4.885	11.9
SiO₂–Al₂O₃–MgO^{[17,29,28-29]}	4.792	?9.176	2.011	19.9
SiO₂–Al₂O₃–CaO^{[21,23-24,30-32]}	3.528	?4.81	2.268	19.6
SiO₂–Al₂O₃–BaO^[17]	?22.607	32.833	?28.33	16.2
SiO₂–Al₂O₃–MnO^[22]	3.233	?4.811	3.519	10.3
SiO₂–Al₂O₃–FeO*^[21,32]	8.671	?29.49	?6.376	19.8
*：Utilize the viscosity values of SiO₂–Al₂O₃–CaO–FeO slag system.

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