Corrosion micro-nano scale kinetics model development and application in non-conventional supercritical boilers

doi:10.11949/0438-1157.20230440

Abstract

Abstract:

Deep and frequent peak shaving supercritical/ultra-supercritical coal-fired boilers of thermal power units will serve in non-conventional conditions with frequent temperature changes and large changes. However, the traditional corrosion kinetic model relies on continuous exposure time at a constant temperature, which is challenging to meet the corrosion prediction and safety assessment of boilers in non-conventional service. According to the fundamental atomic/molecular scale process of corrosion of boiler high-temperature heating tube (in supercritical water environments), this paper proposes a new micro-nano scale kinetic model construction method for the prediction of corrosion in non-conventional conditions and the multi-scale application of the model in macro-corrosion data fitting and micro-scale corrosion process analysis. On this basis, a mechanistic corrosion kinetic model with clear microscopic processes and physical meaning for T92 steel was obtained. And a micro-nano scale oxide film growth rate model with temperature and film thickness as independent variables was developed. Finally, these micro-nano scale kinetic models were employed for the corrosion prediction of boiler tubes with known corrosion levels or/and at frequent variable load (non-constant temperature). It is of tremendous importance for evaluating the safety of large coal-fired boilers in non-conventional service.

Key words: supercritical water, non-conventional boiler corrosion, kinetic model, multiscale, corrosion prediction, growth rate model

摘要：

深度频繁调峰超（超）临界火电机组燃煤锅炉将服役于温度频繁、大幅度多变的非常规条件，然而，依赖于某一恒定温度下连续暴露时间的传统腐蚀动力学模型无法适用于非常规服役锅炉的腐蚀预测及安全评估。从锅炉高温受热面管内（处于超临界水环境）腐蚀的原子/分子尺度过程出发，提出了适用于超（超）临界锅炉非常服役条件的低密度超临界水环境合金腐蚀微纳尺度动力学模型构建方法，以及该模型在宏观腐蚀数据拟合及微尺度腐蚀过程解析方面的多尺度应用途径；获得了典型材料T92钢的微纳尺度腐蚀动力学模型，建立了以温度和膜厚为自变量的微纳尺度氧化膜生长速率模型，并开展超期服役（已知腐蚀程度）、频繁变负荷（非恒定温度）等非常规服役条件下锅炉的腐蚀预测，可为灵活调峰火电机组安全保障技术的开发奠定基础。

关键词: 超临界水, 非常规锅炉腐蚀, 动力学模型, 多尺度, 腐蚀预测, 生长速率模型

CLC Number:

TK 224.9

Yanhui LI, Shaoming DING, Zhouyang BAI, Yinan ZHANG, Zhihong YU, Limei XING, Pengfei GAO, Yongzhen WANG. Corrosion micro-nano scale kinetics model development and application in non-conventional supercritical boilers[J]. CIESC Journal, 2023, 74(6): 2436-2446.

李艳辉, 丁邵明, 白周央, 张一楠, 于智红, 邢利梅, 高鹏飞, 王永贞. 非常规服役超临界锅炉的微纳尺度腐蚀动力学模型建立及应用[J]. 化工学报, 2023, 74(6): 2436-2446.

Figures/Tables 13

Fig.1 Point defect model of metal corrosion in supercritical water at low density for ultra-supercritical thermal power generationvm—vacancy in the metal substrate; VMχ'— cation vacancy; Miχ+—cation interstitial; VÖ —oxygen (anion) vacancy; OO—lattice oxygen within the oxides; MM—cation at the cation sublattice of oxides; MOχ/2/MOδ/2 —barrier / outer layer oxide; MOθ/2(d) — products by further oxidizing outer layer oxide

Table 1 Definition of intermediate parameters for the rate constants of reactions at the 9 atomic/molecular scale interfaces

反应	$a i$ /V^-1	$b i$ /cm^-1	$c i$
R _i (i = 1, 2, 3)	$α i χ γ 1 - α$	$- α i χ γ ε$	$- α i χ γ β$
R _i (i = 4, 5, 6, 7, 8, 9)	0	0	0

Table 1 Definition of intermediate parameters for the rate constants of reactions at the 9 atomic/molecular scale interfaces

反应	$a i$ /V^-1	$b i$ /cm^-1	$c i$
R _i (i = 1, 2, 3)	$α i χ γ 1 - α$	$- α i χ γ ε$	$- α i χ γ β$
R _i (i = 4, 5, 6, 7, 8, 9)	0	0	0

Table 2 Expressions for the standard rate constants and base rate constants for basic interfacial reactions

反应	$k i 0$	$k i 00$
R _i (i = 1,2,3)	$k i 00 e x p - α i χ F φ 0 R T$	$k i 00' e x p - α i Δ G R, i 0 R 1 T - 1 T 0$
R _i (i = 4,5,6,7,8,9)	$k i 00$	$k i 00' e x p - α i Δ G R, i 0 R 1 T - 1 T 0$

Table 2 Expressions for the standard rate constants and base rate constants for basic interfacial reactions

反应	$k i 0$	$k i 00$
R _i (i = 1,2,3)	$k i 00 e x p - α i χ F φ 0 R T$	$k i 00' e x p - α i Δ G R, i 0 R 1 T - 1 T 0$
R _i (i = 4,5,6,7,8,9)	$k i 00$	$k i 00' e x p - α i Δ G R, i 0 R 1 T - 1 T 0$

Table 3 Basic parameters obtained from the optimization of the kinetic model in mass gain for T92 steel at 600℃

符号	参数	数值
T/℃	温度	600
DO/(mg/L)	溶解氧量	0.01
pH	pH	11
$α$	阻挡层/外层界面极化率	0.70
$α 3$	传递系数	0.10
$k 300$ /(mol/(cm²∙s)）	基本速率常数	8.26×10^-11
$k 800$ /(mol/(cm²∙s)）	基本速率常数	9.97×10^-9
$k 900$ /(mol/(cm²∙s)）	基本速率常数	8.55×10^-9
$β$	阻挡层/环境界面处电势降对pH的依赖性	-0.005
V/V	等效腐蚀电位	0.76
ε/(V/cm)	膜内电场强度	128.20
$ρ b l$ /(g/cm³)	阻挡层平均密度	4.97
$ρ o l$ /(g/cm³)	外层平均密度	5.04
PBR	平均Pilling-Bedworth比率	2.08
n、m、q、r	界面反应对氧浓度的动力学级数	0.50

Table 3 Basic parameters obtained from the optimization of the kinetic model in mass gain for T92 steel at 600℃

符号	参数	数值
T/℃	温度	600
DO/(mg/L)	溶解氧量	0.01
pH	pH	11
$α$	阻挡层/外层界面极化率	0.70
$α 3$	传递系数	0.10
$k 300$ /(mol/(cm²∙s)）	基本速率常数	8.26×10^-11
$k 800$ /(mol/(cm²∙s)）	基本速率常数	9.97×10^-9
$k 900$ /(mol/(cm²∙s)）	基本速率常数	8.55×10^-9
$β$	阻挡层/环境界面处电势降对pH的依赖性	-0.005
V/V	等效腐蚀电位	0.76
ε/(V/cm)	膜内电场强度	128.20
$ρ b l$ /(g/cm³)	阻挡层平均密度	4.97
$ρ o l$ /(g/cm³)	外层平均密度	5.04
PBR	平均Pilling-Bedworth比率	2.08
n、m、q、r	界面反应对氧浓度的动力学级数	0.50

Table 4 Macroscopic parameter values of kinetic model in mass gain for T92 at 500—700℃

参数	工况
	500℃^①	600℃		650℃^①	700℃^①
	500℃^①	宏观拟合值^①	微观计算值^②	650℃^①	700℃^①
P₁/(mg/cm²)	0.130	0.130	0.104	0.130	0.130
P₂/(mg/cm²)	-0.98	-2.60	-2.70	-4.30	-5.20
P₃/(mg/(cm²∙s))	4.98×10^-7	6.92×10^-6	6.81×10^-6	2.06×10^-5	3.97×10^-5
P₄/(mg/(cm²∙s))	3.46×10^-8	3.68×10^-8	3.74×10^-8	3.75×10^-8	3.85×10^-8
P₅/(mg/(cm²∙s))	5.41×10^-7	7.22×10^-6	7.38×10^-6	2.23×10^-5	4.31×10^-5
P₆/(mg/(cm²∙s))	3.83×10^-8	4.07×10^-8	4.05×10^-8	4.12×10^-8	4.17×10^-8
P₇/(mg/cm²)	-22.9	-51.0	-55.5	-82.7	-96.2

Fig.2 Fitting curves of P3—P6vs temperature

Table 5 The dependence of macroscopic parameters on temperature in the mass gain kinetic model obtained by direct fitting

参数	关系式
P₁	1.30×10^-4
P₂	$- 0.0011 e x p T 409.95 + 0.0060$
P₃	$1.43 e x p - 16785.74 T$
P₄	$5.80 × 10 - 11 e x p - 395.80 T$
P₅	$1.54 e x p - 16787.19 T$
P₆	$5.86 × 10 - 11 e x p - 324.99 T$
P₇	$- P 5 P 2 P 3 l n P 3 e P 1 P 2 - P 4 + P 1$

Table 5 The dependence of macroscopic parameters on temperature in the mass gain kinetic model obtained by direct fitting

参数	关系式
P₁	1.30×10^-4
P₂	$- 0.0011 e x p T 409.95 + 0.0060$
P₃	$1.43 e x p - 16785.74 T$
P₄	$5.80 × 10 - 11 e x p - 395.80 T$
P₅	$1.54 e x p - 16787.19 T$
P₆	$5.86 × 10 - 11 e x p - 324.99 T$
P₇	$- P 5 P 2 P 3 l n P 3 e P 1 P 2 - P 4 + P 1$

Fig.3 Prediction of T92 corrosion mass gain in 500—700℃ supercritical water based on Table 5

Fig.4 Fitted rate constants vs temperature for the microscopic reaction basis of partial corrosion of steel T92

Table 6 Atomic-scale reaction rate constants and intermediate parameters P1—P7 of the mass gain kinetic model as a function of temperature

参数	关系式	常数
$k 30$	$0.071 e x p - 17841.47 T$	—
$k 8$	$1.21 × 10 - 8 e x p - 165.63 T$	—
$k 9$	$1.23 × 10 - 8 e x p - 316.02 T$	—
ε	$2.48 × 106 e x p - T 83.99 + 48.41$	—
P₁	1.04×10^-4	—
P₂	$C 1 T ε$	$C 1 = - 4.00 × 10 - 4$
P₃	$C 2 k 30 e x p 993.16 T$	$C 2 = 21.21$
P₄	$C 3 k 8$	$C 3 = 37.50 × 10 - 4$
P₅	$C 4 k 30 e x p 993.16 T$	$C 4 = 23.00$
P₆	$C 5 k 8 + C 6 k 9$	$C 5 = 40.65 × 10 - 4$ $C 6 = 37.64 × 10 - 4$
P₇	$- P 5 P 2 P 3 l n P 3 e P 1 P 2 - P 4 + P 1$	—

Table 6 Atomic-scale reaction rate constants and intermediate parameters P1—P7 of the mass gain kinetic model as a function of temperature

参数	关系式	常数
$k 30$	$0.071 e x p - 17841.47 T$	—
$k 8$	$1.21 × 10 - 8 e x p - 165.63 T$	—
$k 9$	$1.23 × 10 - 8 e x p - 316.02 T$	—
ε	$2.48 × 106 e x p - T 83.99 + 48.41$	—
P₁	1.04×10^-4	—
P₂	$C 1 T ε$	$C 1 = - 4.00 × 10 - 4$
P₃	$C 2 k 30 e x p 993.16 T$	$C 2 = 21.21$
P₄	$C 3 k 8$	$C 3 = 37.50 × 10 - 4$
P₅	$C 4 k 30 e x p 993.16 T$	$C 4 = 23.00$
P₆	$C 5 k 8 + C 6 k 9$	$C 5 = 40.65 × 10 - 4$ $C 6 = 37.64 × 10 - 4$
P₇	$- P 5 P 2 P 3 l n P 3 e P 1 P 2 - P 4 + P 1$	—

Fig.5 Verification of the micro-nano scale oxidation mass gain model of steel T92 based on the kinetics of the micro-nano corrosion reactions

Fig.6 Application of oxide film growth rate model for corrosion prediction for in-service or intended to be extended service boilers with certain degree of corrosion

Fig.7 Prediction of corrosion mass gain for cyclic oxidation of T92 at 550 and 600℃

References 31

1	谭增强, 王一坤, 牛拥军, 等. 双碳目标下煤电深度调峰及调频技术研究进展[J]. 热能动力工程, 2022, 37(8): 1-8.
	Tan Z Q, Wang Y K, Niu Y J, et al. Research progress of deep peak regulation and frequency modulation technology for coal-fired power plant under double-carbon targets[J]. Journal of Engineering for Thermal Energy and Power, 2022, 37(8): 1-8.
2	周科, 何敏强, 牛田田, 等. 超临界660 MW褐煤锅炉深度调峰负荷水动力特性研究[J]. 热力发电, 2022, 51(9): 88-95.
	Zhou K, He M Q, Niu T T, et al. Research on hydrodynamic characteristics at deep peak load regulation of 660 MW supercritical lignite boiler[J]. Thermal Power Generation, 2022, 51(9): 88-95.
3	吴鹏举, 朱超, 万李, 等. 超临界机组锅炉20%负荷深度调峰水动力实炉试验研究[J]. 热力发电, 2021, 50(4): 59-66.
	Wu P J, Zhu C, Wan L, et al. Actual furnace test research on hydrodynamics of a supercritical boiler at 20% deep peak load[J]. Thermal Power Generation, 2021, 50(4): 59-66.
4	欧阳诗洁, 李娟, 董乐, 等. 超超临界锅炉低负荷运行时的流动不稳定性计算分析[J]. 西安交通大学学报, 2019, 53(7): 84-91.
	Ouyang S J, Li J, Dong L, et al. Calculation and analysis on the flow instability of an ultra supercritical boiler under low load[J]. Journal of Xi'an Jiaotong University, 2019, 53(7): 84-91.
5	边彩霞, 周克毅, 朱正林, 等. 停机过程中锅炉高温受热面蒸汽侧氧化膜的应力分析[J]. 化工学报, 2013, 64(4): 1444-1452.
	Bian C X, Zhou K Y, Zhu Z L, et al. Numerical analysis of stresses of steam-side oxide scales in boiler high-temperature heating surface in shutdown process[J]. CIESC Journal, 2013, 64(4): 1444-1452.
6	李海燕, 刘欢, 张秀菊, 等. HVOF喷涂用于提高锅炉换热面耐磨损耐腐蚀性能综述[J]. 化工学报, 2021, 72(4): 1833-1846.
	Li H Y, Liu H, Zhang X J, et al. Summary of improving erosion and corrosion resistance of heat exchange surfaces in boilers through HVOF technology[J]. CIESC Journal, 2021, 72(4): 1833-1846.
7	Gómez-Briceño D, Blázquez F, Sáez-Maderuelo A. Oxidation of austenitic and ferritic/martensitic alloys in supercritical water[J]. The Journal of Supercritical Fluids, 2013, 78: 103-113.
8	Guan X, MacDonald D D. Determination of corrosion mechanisms and estimation of electrochemical kinetics of metal corrosion in high subcritical and supercritical aqueous systems[J]. Corrosion, 2009, 65(6): 376-387.
9	Guzonas D A, Cook W G. Cycle chemistry and its effect on materials in a supercritical water-cooled reactor: a synthesis of current understanding[J]. Corrosion Science, 2012, 65: 48-66.
10	Kritzer P. Corrosion in high-temperature and supercritical water and aqueous solutions: a review[J]. The Journal of Supercritical Fluids, 2004, 29(1/2): 1-29.
11	Li Y H, Xu T T, Wang S Z, et al. Characterization of oxide scales formed on heating equipment in supercritical water gasification process for producing hydrogen[J]. International Journal of Hydrogen Energy, 2019, 44(56): 29508-29515.
12	MacDonald D D, Guan X. Volume of activation for the corrosion of type 304 stainless steel in high subcritical and supercritical aqueous systems[J]. Corrosion, 2009, 65(7): 427-437.
13	沈朝, 汪家梅, 张乐福. 镍基合金C276在超临界水中的腐蚀行为[J]. 工程科学学报, 2016, 38(5): 706-713.
	Shen Z, Wang J M, Zhang L F. Corrosion behavior of Ni-base alloy C276 in supercritical water[J]. Chinese Journal of Engineering, 2016, 38(5): 706-713.
14	张洁, 曲积钰, 卢金玲, 等. 亚临界/超临界水条件下镍基合金(Incoloy800, 825, 625)的硫化腐蚀特性研究[J]. 中国腐蚀与防护学报, 2021, 41(6): 892-898.
	Zhang J, Qu J Y, Lu J L, et al. Sulfidation corrosion behavior of nickel-based alloys(Incoloy800, 825 and 625) in sub/supercritical water[J]. Journal of Chinese Society for Corrosion and Protection, 2021, 41(6): 892-898.
15	Zhang N Q, Yue G Q, Lv F B, et al. Oxidation of low-alloy steel in high temperature steam and supercritical water[J]. Materials at High Temperatures, 2017, 34(3): 222-228.
16	Li Y H, Wang S Z, Sun P P, et al. Early oxidation mechanism of austenitic stainless steel TP347H in supercritical water[J]. Corrosion Science, 2017, 128: 241-252.
17	Zhu Z L, Xu H, Jiang D F, et al. Influence of temperature on the oxidation behaviour of a ferritic-martensitic steel in supercritical water[J]. Corrosion Science, 2016, 113: 172-179.
18	Li Y H, Wang S Z, Sun P P, et al. Investigation on early formation and evolution of oxide scales on ferritic-martensitic steels in supercritical water[J]. Corrosion Science, 2018, 135: 136-146.
19	Zhu Z L, Xu H, Jiang D F, et al. Temperature dependence of oxidation behaviour of a ferritic-martensitic steel in supercritical water at 600—700℃[J]. Oxidation of Metals, 2016, 86(5/6): 483-496.
20	Bischoff J, Motta A T. Oxidation behavior of ferritic-martensitic and ODS steels in supercritical water[J]. Journal of Nuclear Materials, 2012, 424(1/2/3): 261-276.
21	Fromhold A T J, Fromhold R G. Chapter 1: an overview of metal oxidation theory[M]//Reactions of Solids with Gases. Amsterdam: Elsevier, 1984: 1-117.
22	Atkinson A. Transport processes during the growth of oxide films at elevated temperature[J]. Reviews of Modern Physics, 1985, 57(2): 437-470.
23	Li Y H, Wang S Z, Xu T T, et al. Novel designs for the reliability and safety of supercritical water oxidation process for sludge treatment[J]. Process Safety and Environmental Protection, 2021, 149: 385-398.
24	Li Y H, MacDonald D D, Yang J, et al. Point defect model for the corrosion of steels in supercritical water(part Ⅰ): Film growth kinetics[J]. Corrosion Science, 2020, 163: 108280.
25	Li Y H, Xu T T, Wang S Z, et al. Predictions and analyses on the growth behavior of oxide scales formed on ferritic-martensitic in supercritical water[J]. Oxidation of Metals, 2019, 92(1/2): 27-48.
26	王起江, 洪杰, 徐松乾, 等. 超超临界电站锅炉用关键材料[J]. 北京科技大学学报, 2012, 34(S1): 26-33.
	Wang Q J, Hong J, Xu S Q, et al. Key materials used in ultra-supercritical power station boilers[J]. Journal of University of Science and Technology Beijing, 2012, 34(S1): 26-33.
27	于鸿垚, 迟成宇, 董建新, 等. 650℃长期时效过程中Super304H耐热不锈钢组织的演变[J]. 北京科技大学学报, 2010, 32(7): 877-882.
	Yu H Y, Chi C Y, Dong J X, et al. Microstructural evolution of heat-resistant steel Super304H during 650℃ long term aging[J]. Journal of University of Science and Technology Beijing, 2010, 32(7): 877-882.
28	Dudziak T, Łukaszewicz M, Simms N, et al. Analysis of high temperature steam oxidation of superheater steels used in coal fired boilers[J]. Oxidation of Metals, 2016, 85(1): 171-187.
29	尹开锯, 邱绍宇, 唐睿, 等. 铁素体-马氏体钢P91和P92在超临界水中腐蚀后氧化膜多孔性分析[J]. 中国腐蚀与防护学报, 2010, 30(1): 1-5.
	Yin K J, Qiu S Y, Tang R, et al. Characterization of the porosity of the oxide scales on ferritic-martensitic steel P91 and P92 exposed in supercritical water[J]. Journal of Chinese Society for Corrosion and Protection, 2010, 30(1): 1-5.
30	Tan L, Ren X, Allen T R. Corrosion behavior of 9%—12% Cr ferritic-martensitic steels in supercritical water[J]. Corrosion Science, 2010, 52(4): 1520-1528.
31	Was G S, Ampornrat P, Gupta G, et al. Corrosion and stress corrosion cracking in supercritical water[J]. Journal of Nuclear Materials, 2007, 371(1/2/3): 176-201.

[1]	Zhenghao JIN, Lijie FENG, Shuhong LI. Energy and exergy analysis of a solution cross-type absorption-resorption heat pump using NH₃/H₂O as working fluid [J]. CIESC Journal, 2023, 74(S1): 53-63.
[2]	Zhewen CHEN, Junjie WEI, Yuming ZHANG. System integration and energy conversion mechanism of the power technology with integrated supercritical water gasification of coal and SOFC [J]. CIESC Journal, 2023, 74(9): 3888-3902.
[3]	Jintong LI, Shun QIU, Wenshou SUN. Oxalic acid and UV enhanced arsenic leaching from coal in flue gas desulfurization by coal slurry [J]. CIESC Journal, 2023, 74(8): 3522-3532.
[4]	Haopeng SHI, Dawen ZHONG, Xuexin LIAN, Junfeng ZHANG. Experimental study on the downward-facing surface enhanced boiling heat transfer of multiscale groove-fin structures [J]. CIESC Journal, 2023, 74(7): 2880-2888.
[5]	Ming DONG, Jinliang XU, Guanglin LIU. Molecular dynamics study on heterogeneous characteristics of supercritical water [J]. CIESC Journal, 2023, 74(7): 2836-2847.
[6]	Chengze WANG, Kaili GU, Jinhua ZHANG, Jianxuan SHI, Yiwei LIU, Jinxiang LI. Sulfidation couples with aging to enhance the reactivity of zerovalent iron toward Cr(Ⅵ) in water [J]. CIESC Journal, 2023, 74(5): 2197-2206.
[7]	Jieyuan ZHENG, Xianwei ZHANG, Jintao WAN, Hong FAN. Synthesis and curing kinetic analysis of eugenol-based siloxane epoxy resin [J]. CIESC Journal, 2023, 74(2): 924-932.
[8]	Huan ZHOU, Mengli ZHANG, Qing HAO, Si WU, Jie LI, Cunbing XU. Process mechanism and dynamic behaviors of magnesium sulfate type carnallite converting into kainite [J]. CIESC Journal, 2022, 73(9): 3841-3850.
[9]	Yujun MA, Xiangjun LIU. Theoretical studies of water recovery from flue gas by using ceramic membrane [J]. CIESC Journal, 2022, 73(9): 4103-4112.
[10]	Xingang QI, Libo LU, Yunan CHEN, Zhiwei GE, Liejin GUO. Review of black liquor supercritical water gasification for hydrogen production with high value-added chemicals recovery [J]. CIESC Journal, 2022, 73(8): 3338-3354.
[11]	Pei WANG, Rongkuo WEI. Thermal-mass nonequilibrium model for water splitting hydrogen production by solar thermochemical cycle of porous cerium oxide [J]. CIESC Journal, 2022, 73(7): 2885-2894.
[12]	Wei LIU, Yan SUN. Research progress on amyloid β-protein aggregation and its regulation [J]. CIESC Journal, 2022, 73(6): 2381-2396.
[13]	Shanwei HU, Xinhua LIU. Multiscale trans-regime EMMS modeling of gas-solid fluidization systems [J]. CIESC Journal, 2022, 73(6): 2514-2528.
[14]	Zhihao HUANG, Guangxi LI, Guihua TANG, Xiaolong LI, Yuanhong FAN. Numerical investigation on heat transfer of supercritical water in a side-heated square channel [J]. CIESC Journal, 2022, 73(4): 1523-1533.
[15]	Qianshi SONG, Xiaowei WANG, Wei ZHANG, Xiaohan WANG, Haowen LI, Yu QIAO. Catalytic/inhibitory effects of inorganic elements on biomass char-CO₂ gasification reactivity and model construction [J]. CIESC Journal, 2022, 73(11): 5240-5250.