Pore evolution and its influence on volatile mass transfer during long-flame coal pyrolysis

doi:10.11949/0438-1157.20250512

Abstract

Abstract:

Pore structure is one of the important factors affecting pyrolytic devolatiles. This study systematically investigates the evolution and fractal characteristics of semicoke pores at different pyrolysis final temperatures (393—1073 K) using integrated N₂ adsorption and fractal dimension analysis. A particle-scale model was developed based on pore evolution patterns, incorporating tar secondary cracking, volatile diffusion in fractal pores, and predicting transient temperature distribution, volatile yields, and pore structure changes. The results show that slit-shaped mesopores dominate during semi-coke pyrolysis, with pore evolution driven by drying degassing, organic decomposition with pore shrinkage, and increased heterogeneity from micropores. Pore structure mainly influences volatile yields by modifying tar diffusion pathways, while showing negligible effects on light gas production. This work provides fundamental insights into pore-volatile interactions that are crucial for pyrolysis reactor design and process optimization.

Key words: low-rank coal pyrolysis, porous media, pore distribution, fractal dimension, diffusion, numerical simulation

摘要：

孔隙结构是影响热解脱挥发分的重要因素之一。为了研究煤热解过程中孔隙的演变规律和分形特征及其对挥发分传质行为的影响，本文通过N₂吸附法和分形理论对不同热解终温（393~1073 K）下半焦的孔隙结构进行了分析和定量描述。并基于半焦孔隙的演变规律和分形特征，从颗粒尺度上对热解过程中孔结构的演变进行了建模，模型考虑了焦油的二次裂解反应、挥发分在分形孔隙内的扩散，同时能预测煤颗粒的瞬态温度分布、挥发分的生成以及孔隙结构的变化。结果表明，半焦热解过程中以狭缝状介孔为主；影响孔隙演变的机制包括干燥脱气、有机质裂解与孔隙收缩；微孔存在增加了半焦孔结构的非均质性。孔结构主要通过改变焦油的扩散机制来影响挥发分的产率，对轻质气体的产率影响不大。

关键词: 低阶煤热解, 多孔介质, 孔隙结构, 分形维数, 扩散, 数值模拟

CLC Number:

TQ 021.4

Yi CUI, Yaowei HU, Yuncai SONG, Jie FENG, Wenying LI. Pore evolution and its influence on volatile mass transfer during long-flame coal pyrolysis[J]. CIESC Journal, 2025, 76(10): 5300-5310.

崔诣, 胡耀伟, 宋云彩, 冯杰, 李文英. 长焰煤热解过程中孔的演变及其对挥发分传质影响[J]. 化工学报, 2025, 76(10): 5300-5310.

Figures/Tables 15

Table 1 Proximate and ultimate analysis of CJT

工业分析w_ad/%				元素分析w_daf/%
M	A	V	FC	C	H	N	S	O
2.80	7.80	35.38	54.02	81.62	5.64	1.05	0.82	9.81

Fig.1 Illustration of single-particle coal pyrolysis model

Table 2 Mathematical modeling involved in the reaction process

方程类别	方程
能量守恒方程^[19]	$ρ c p e f f ∂ T ∂ t ︸累积项 + ρ c p g, m i x 1 r 2 ∂ ∂ r r 2 u T ︸对流项 + 1 r 2 ∂ ∂ r - r 2 λ e f f ∂ T ∂ t ︸传热项 = Q t o t ︸热源项$
有效比热容(ρc_p )_eff	$ρ c p e f f = 1 - ε c p, a ρ a + c p, i s ρ i s + c p, c ρ c + ε ρ c p g, m i x$
有效热导率λ_eff	$λ e f f = 1 - ε λ a ρ a + λ i s ρ i s + λ c ρ c ρ a + ρ i s + ρ c + ε λ g, m i x + 13.5 σ T 3 d p e w$
热源项Q_tot^[20]	$Q t o t = - k t Δ H t + k g Δ H g + k i s Δ H i s ρ a - k c Δ H c ρ i s - k g 1 Δ H g 1 + k c 1 Δ H c 1 ρ t$
局部热通量q^[21]	$q = - λ e f f ∇ T + h d Δ T$
动量传递控制方程^[22]	$∂ ε ρ g, m i x ∂ t + ∇ ⋅ ρ g, m i x u = Q m$
气体流速u	$u = - κ μ g, m i x ∂ p ∂ r$
多孔基体的渗透率κ^[23]	$κ = ε 3 180 1 - ε 2 d p e 2$
理想气体状态方程^[24]	$ρ g, m i x = ∑ i ρ i$ , $p = ρ g, m i x R T M g, m i x$ , $M g, m i x = ∑ i ρ i ρ g, m i x M i - 1$
质量传递方程^[25]	$∂ ε c i ∂ t ︸累积项 + 1 r 2 ∂ r 2 c i u ∂ r ︸对流项 + 1 r 2 ∂ r 2 J i ∂ r ︸扩散项 = R i ︸源项$
对流质量通量^[20]	$T a r : ∂ ε ρ t ∂ t + 1 r 2 ∂ r 2 V ρ t ∂ t = k t ρ a - k c 1 + k g 1 ρ t$ , $G a s : ∂ ε ρ g ∂ t + 1 r 2 ∂ r 2 V ρ g ∂ t = k g ρ a + k g 1 ρ t$
扩散通量J_i^[26]	$J i = - D i ∇ c i$
分形扩散系数D_i^[27]	$D i = v 3 d p 0.0033 d p δ + 0.57 e - 7.05 - 0.054 D f d p δ ε 2.97 - 0.17 d p δ$
分子运动的平均速率v^[27]	$v = 8 R T π M i$
分子平均自由程δ^[28]	$δ = κ B T 2 p π d m 2$
孔隙结构演变模型^{[14, 19, 27, 29]}	$V s o l i d V 0, a = ρ a + α ρ i s + ρ c ρ 0, a$ , $V p = V 0, p + β V 0, a - V s o l i d$ , $V f i n a l, p = γ V 0, p 0$ $V 0 . p = θ V 0, p 0 + 1 - θ V f i n a l, p$ , $θ = ρ a ρ 0, a$ , $V p e = V + s o l i d V p$ , $ε = V p V p e$ $d p = d 0, p ε 1 / 3$ , $l p = χ d p 2 ε 1 / 3$ , $D f = - l n d S p d r p l n r p$ , $S p = 4 ε V p e d p 1 - ε$
Nusselt数^[30-31]	$N u = 2.0 + f × R e 1 / 2 P r 1 / 3$
Reynolds数^[32]	$R e = ρ g d p u μ g$
Prandtl数^[32]	$P r = μ g c p, g λ g$
反应速率常数k^[18]	$k = A i e - E i R T$

Table 2 Mathematical modeling involved in the reaction process

方程类别	方程
能量守恒方程^[19]	$ρ c p e f f ∂ T ∂ t ︸累积项 + ρ c p g, m i x 1 r 2 ∂ ∂ r r 2 u T ︸对流项 + 1 r 2 ∂ ∂ r - r 2 λ e f f ∂ T ∂ t ︸传热项 = Q t o t ︸热源项$
有效比热容(ρc_p )_eff	$ρ c p e f f = 1 - ε c p, a ρ a + c p, i s ρ i s + c p, c ρ c + ε ρ c p g, m i x$
有效热导率λ_eff	$λ e f f = 1 - ε λ a ρ a + λ i s ρ i s + λ c ρ c ρ a + ρ i s + ρ c + ε λ g, m i x + 13.5 σ T 3 d p e w$
热源项Q_tot^[20]	$Q t o t = - k t Δ H t + k g Δ H g + k i s Δ H i s ρ a - k c Δ H c ρ i s - k g 1 Δ H g 1 + k c 1 Δ H c 1 ρ t$
局部热通量q^[21]	$q = - λ e f f ∇ T + h d Δ T$
动量传递控制方程^[22]	$∂ ε ρ g, m i x ∂ t + ∇ ⋅ ρ g, m i x u = Q m$
气体流速u	$u = - κ μ g, m i x ∂ p ∂ r$
多孔基体的渗透率κ^[23]	$κ = ε 3 180 1 - ε 2 d p e 2$
理想气体状态方程^[24]	$ρ g, m i x = ∑ i ρ i$ , $p = ρ g, m i x R T M g, m i x$ , $M g, m i x = ∑ i ρ i ρ g, m i x M i - 1$
质量传递方程^[25]	$∂ ε c i ∂ t ︸累积项 + 1 r 2 ∂ r 2 c i u ∂ r ︸对流项 + 1 r 2 ∂ r 2 J i ∂ r ︸扩散项 = R i ︸源项$
对流质量通量^[20]	$T a r : ∂ ε ρ t ∂ t + 1 r 2 ∂ r 2 V ρ t ∂ t = k t ρ a - k c 1 + k g 1 ρ t$ , $G a s : ∂ ε ρ g ∂ t + 1 r 2 ∂ r 2 V ρ g ∂ t = k g ρ a + k g 1 ρ t$
扩散通量J_i^[26]	$J i = - D i ∇ c i$
分形扩散系数D_i^[27]	$D i = v 3 d p 0.0033 d p δ + 0.57 e - 7.05 - 0.054 D f d p δ ε 2.97 - 0.17 d p δ$
分子运动的平均速率v^[27]	$v = 8 R T π M i$
分子平均自由程δ^[28]	$δ = κ B T 2 p π d m 2$
孔隙结构演变模型^{[14, 19, 27, 29]}	$V s o l i d V 0, a = ρ a + α ρ i s + ρ c ρ 0, a$ , $V p = V 0, p + β V 0, a - V s o l i d$ , $V f i n a l, p = γ V 0, p 0$ $V 0 . p = θ V 0, p 0 + 1 - θ V f i n a l, p$ , $θ = ρ a ρ 0, a$ , $V p e = V + s o l i d V p$ , $ε = V p V p e$ $d p = d 0, p ε 1 / 3$ , $l p = χ d p 2 ε 1 / 3$ , $D f = - l n d S p d r p l n r p$ , $S p = 4 ε V p e d p 1 - ε$
Nusselt数^[30-31]	$N u = 2.0 + f × R e 1 / 2 P r 1 / 3$
Reynolds数^[32]	$R e = ρ g d p u μ g$
Prandtl数^[32]	$P r = μ g c p, g λ g$
反应速率常数k^[18]	$k = A i e - E i R T$

Table 3 Kinetic parameters and reaction heat of pyrolysis reactions［20］

反应	指前因子A_i /s^-1	活化能E_i /(kJ·mol^-1)	反应热ΔH/(kJ·kg^-1)
1	4.38×10⁹	152.7	80
2	1.08×10¹⁰	148	80
3	3.75×10⁶	111.7	80
4	4.28×10⁶	108	-42
5	1×10⁵	108	-42
6	1.38×10¹⁰	161	-300

Fig.2 Pyrolytic reaction pathways

Table 4 Physical property parameters or relationships used in the model［33］

物性参数	数值或表达式
比热容/(J·kg^-1·K^-1)	$c p, a = 1150 T ≤ 573 K 1150 + 2.03 T - 573 - 1.55 × 10 - 3 T - 573 2 T > 573 K$ $c p, i s = c p, c = 1458$ , $c p g, m i x = 1390$
热导率/(W·m^-1·K^-1)	$λ a = 0.23 T ≤ 673 K 0.23 + 2.24 × 10 - 5 T - 673 1.8 T > 673 K$ $λ i s = λ c = 1.89$ , $λ g, m i x = 0.07$
颗粒的初始密度/ (kg·m^-3)	$ρ 0, a = 1250$
环境压力/Pa	$p a m b = 101325$

Table 4 Physical property parameters or relationships used in the model［33］

物性参数	数值或表达式
比热容/(J·kg^-1·K^-1)	$c p, a = 1150 T ≤ 573 K 1150 + 2.03 T - 573 - 1.55 × 10 - 3 T - 573 2 T > 573 K$ $c p, i s = c p, c = 1458$ , $c p g, m i x = 1390$
热导率/(W·m^-1·K^-1)	$λ a = 0.23 T ≤ 673 K 0.23 + 2.24 × 10 - 5 T - 673 1.8 T > 673 K$ $λ i s = λ c = 1.89$ , $λ g, m i x = 0.07$
颗粒的初始密度/ (kg·m^-3)	$ρ 0, a = 1250$
环境压力/Pa	$p a m b = 101325$

Table 5 Physical parameters of volatiles components of coal pyrolysis［34］

挥发分组成

摩尔质量M/

(kg·mol^-1)

有效分子碰撞

直径d_m/m

3.79×10^-5, T_0,gas=298 K

Fig.3 Isothermal curves of N2 adsorption/desorption of semi-coke at different pyrolysis temperature

Fig.4 Evolution of semi-coke pore structure

Table 6 Pore volume of semicoke at different pyrolysis temperature

热解温度/K	微孔孔容/ (cm³·g^-1)	介孔孔容/ (cm³·g^-1)	大孔孔容/ (cm³·g^-1)
393	0.0018	0.0185	0.0109
473	0.0017	0.0217	0.0111
573	0.0017	0.0162	0.0094
673	0.0071	0.0240	0.014
773	0.0144	0.0321	0.0161
873	0.0400	0.0428	0.0183
973	0.0543	0.0407	0.0286
1073	0.0216	0.0346	0.0215

Fig.5 Variation of the fractal dimension DFHH-1 and DFHH-2 at different pyrolysis temperature

Fig.6 Comparison between model predictions and experimental results of particle temperature and porosity under different operating conditions

Fig.7 Knudsen number of pyrolyzed light gas and tar in different pore size

Fig.8 Effect of fractal dimension on pyrolysis of light gases with tar yields

Fig.9 Effect of porosity on pyrolysis light gas and tar yields

References 41

[8]	Hu S, Li M, Xiang J, et al. Fractal characteristic of three Chinese coals[J]. Fuel, 2004, 83(10): 1307-1313.
[9]	Lu G W, Wang J L, Wei C T, et al. Pore fractal model applicability and fractal characteristics of seepage and adsorption pores in middle rank tectonic deformed coals from the Huaibei coal field[J]. Journal of Petroleum Science and Engineering, 2018, 171: 808-817.
[10]	Liu X F, Nie B S. Fractal characteristics of coal samples utilizing image analysis and gas adsorption[J]. Fuel, 2016, 182: 314-322.
[11]	Wang F, Cheng Y P, Lu S Q, et al. Influence of coalification on the pore characteristics of middle-high rank coal[J]. Energy & Fuels, 2014, 28(9): 5729-5736.
[12]	Yao Y B, Liu D M, Tang D Z, et al. Fractal characterization of adsorption-pores of coals from North China: an investigation on CH₄ adsorption capacity of coals[J]. International Journal of Coal Geology, 2008, 73(1): 27-42.
[13]	Shi J Q, Durucan S. A bidisperse pore diffusion model for methane displacement desorption in coal by CO₂ injection[J]. Fuel, 2003, 82(10): 1219-1229.
[14]	Simons G A. Coal pyrolysis ( Ⅰ ) : Pore evolution theory[J]. Combustion and Flame, 1983, 53(1/2/3): 83-92.
[15]	Li S F, Yang H, Fletcher T H, et al. Model for the evolution of pore structure in a lignite particle during pyrolysis[J]. Energy & Fuels, 2015, 29(8): 5322-5333.
[16]	Guo F H, Zhao X, Guo Y, et al. Fractal analysis and pore structure of gasification fine slag and its flotation residual carbon[J]. Colloids and Surfaces A: Physicochemical and Engineering Aspects, 2020, 585: 124148.
[17]	Tang J W, Feng L, Li Y J, et al. Fractal and pore structure analysis of Shengli lignite during drying process[J]. Powder Technology, 2016, 303: 251-259.
[18]	Shi X G, Gao J S, Lan X Y. Modeling the pyrolysis of a centimeter-sized biomass particle[J]. Chemical Engineering & Technology, 2019, 42(12): 2574-2579.
[19]	Di Blasi C. Heat, momentum and mass transport through a shrinking biomass particle exposed to thermal radiation[J]. Chemical Engineering Science, 1996, 51(7): 1121-1132.
[1]	Wang Z D, Jiang P F, Yang F, et al. Study on pore structure and fractal characteristics of tar-rich coal during pyrolysis by mercury intrusion porosimetry (MIP)[J]. Geofluids, 2022, 2022: 2067228.
[2]	Chen Y L, Ma L, He R. Development of improved lattice fragmentation and diffusion model for coal pyrolysis(part 1): Steady-state intra-porous gas diffusivity[J]. Combustion Science and Technology, 2014, 186(6): 747-765.
[3]	Solomon P R, Serio M A, Despande G V, et al. Cross-linking reactions during coal conversion[J]. Energy & Fuels, 1990, 4(1): 42-54.
[4]	Ma L Y, Zhang L, Wang D M, et al. Pore structure evolution during lean-oxygen combustion of pyrolyzed residual from low-rank coal and its effect on internal oxygen diffusion mechanism[J]. Fuel, 2022, 319: 123850.
[5]	Sun L N, Tuo J C, Zhang M F, et al. Formation and development of the pore structure in Chang 7 member oil-shale from Ordos Basin during organic matter evolution induced by hydrous pyrolysis[J]. Fuel, 2015, 158: 549-557.
[6]	Xu P, Chen Z Y, Qiu S X, et al. An analytical model for pore and tortuosity fractal dimensions of porous media[J]. Fractals, 2021, 29(6): 2150156-20.
[7]	Li H J, Chang Q H, Gao R, et al. Fractal characteristics and reactivity evolution of lignite during the upgrading process by supercritical CO₂ extraction[J]. Applied Energy, 2018, 225: 559-569.
[20]	Park W C, Atreya A, Baum H R. Experimental and theoretical investigation of heat and mass transfer processes during wood pyrolysis[J]. Combustion and Flame, 2010, 157(3): 481-494.
[21]	Li S N, Cao B Y. Vortex characteristics in Fourier and non-Fourier heat conduction based on heat flux rotation[J]. International Journal of Heat and Mass Transfer, 2017, 108: 2403-2407.
[22]	Atangana A. Fractional variable order derivatives//Fractional Operators with Constant and Variable Order with Application to Geo-hydrology[M]. Pittsburgh: Academic Press, 2018: 221-243.
[23]	Dallavalle J M. Book reviews: flow of gases through porous media[J]. Science, 1956, 124(3234): 1254-1255.
[24]	Grønli M G, Melaaen M C. Mathematical model for wood pyrolysis comparison of experimental measurements with model predictions[J]. Energy & Fuels, 2000, 14(4): 791-800.
[25]	曾子粤, 杨建森, 魏永起. 脱硫石膏灌芯墙脱水过程的仿真模拟与分析[J]. 材料导报, 2022, 36(5): 89-94.
	Zeng Z Y, Yang J S, Wei Y Q. The simulation and analysis of dehydration process of FGD gypsum grouted wall[J]. Materials Reports, 2022, 36(5): 89-94.
[26]	Flores R M. Coal and Coalbed Gas: Fueling the Future[M]. Amsterdam, Netherlands: Elsevier Science, 2013.
[27]	马亮, 何榕. 分形多孔介质中气体稳态扩散[J]. 清华大学学报(自然科学版), 2013, 53(10): 1459-1463.
	Ma L, He R. Steady-state gas diffusion in fractal porous media[J]. Journal of Tsinghua University (Science and Technology), 2013, 53(10): 1459-1463.
[28]	Zhang L Z. A fractal model for gas permeation through porous membranes[J]. International Journal of Heat and Mass Transfer, 2008, 51(21/22): 5288-5295.
[29]	Gómez M A, Porteiro J, Chapela S, et al. An Eulerian model for the simulation of the thermal conversion of a single large biomass particle[J]. Fuel, 2018, 220: 671-681.
[30]	Adesanya B A, Pham H N. Mathematical modelling of devolatilization of large coal particles in a convective environment[J]. Fuel, 1995, 74(6): 896-902.
[31]	Wakao N, Kaguei S, Funazkri T. Effect of fluid dispersion coefficients on particle-to-fluid heat transfer coefficients in packed beds: correlation of nusselt numbers[J]. Chemical Engineering Science, 1979, 34(3): 325-336.
[32]	李方舟, 李文英, 冯杰. 固体热载体法褐煤热解过程中的传质传热特性[J]. 化工学报, 2016, 67(4): 1136-1144.
	Li F Z, Li W Y, Feng J. Characteristics of mass and heat transfer in lignite pyrolysis with solid heat carrier[J]. CIESC Journal, 2016, 67(4): 1136-1144.
[33]	Li F Z, Feng J, Li X H, et al. A model of devolatilization behavior in lignite pyrolysis with solid heat carriers[J]. AIChE Journal, 2019, 65(6): e16590.
[34]	Bliek A, Van Poelje W M, Van Swaaij W P M, et al. Effects of intraparticle heat and mass transfer during devolatilization of a single coal particle[J]. AIChE Journal, 1985, 31(10): 1666-1681.
[35]	Wang J, Ku X K, Liu Z W. Three-dimensional simulation of the pyrolysis of a thermally thick biomass particle[J]. Energy & Fuels, 2023, 37(6): 4413-4428.
[36]	Sing K S W. Reporting physisorption data for gas/solid systems with special reference to the determination of surface area and porosity (Recommendations 1984)[J]. Pure and Applied Chemistry, 1985, 57(4): 603-619.
[37]	Gregg S J, Sing K S W, Salzberg H W. Adsorption surface area and porosity[J]. Journal of the Electrochemical Society, 1967, 114(11): 279C.
[38]	Jia L, Fan B G, Li B, et al. Effects of pyrolysis mode and particle size on the microscopic characteristics and mercury adsorption characteristics of biomass char[J]. BioResources, 2018, 13(3): 5450-5471.
[39]	Zhang F C, Tavakkol S, Galeazzo F C C, et al. Particle-resolved simulation of the pyrolysis process of a single plastic particle[J]. Heat and Mass Transfer, 2024, 61(1): 12.
[40]	Mou P W, Pan J N, Niu Q H, et al. Coal pores: methods, types, and characteristics[J]. Energy & Fuels, 2021, 35(9): 7467-7484.
[41]	柏静儒, 林卫生, 潘朔, 等. 油页岩低温热解过程中轻质气体的析出特性[J]. 化工学报, 2015, 66(3): 1104-1110.
	Bai J R, Lin W S, Pan S, et al. Characteristics of light gases evolution during oil shale pyrolysis[J]. CIESC Journal, 2015, 66(3): 1104-1110.