Sensitivity analysis of model parameters and process operation for batch cooling crystallization process

doi:10.11949/0438-1157.20240627

Abstract

Abstract:

The study aimed to analyze the uncertainties associated with kinetic model parameters and operating parameters in the crystallization model. Three simplified crystallization process models, based on the population balance equations, were considered to analyze the batch cooling crystallization process. The sensitivity of the parameters to the product crystal size distribution (CSD) and the formation of fine crystals was evaluated. The local and global sensitivities of 12 parameters to the three crystallization process models of crystal growth (CG), crystal growth-nucleation (CGN) and crystal growth-nucleation-dissolution (CGND) were quantitatively analyzed, while the convergence of the modified Morris screening method and PAWN method was ensured. And the parameter sensitivities were sorted. The results show that the sensitivity of parameters is different for model situations of different complexity. For product CSD, the parameters μ, C₀, b, and m₀ exhibit significant sensitivity in CG and CGN, while all parameters are insensitive in CGND. For fine crystals, the parameters b, g, and C₀ exhibit significant sensitivity in CGN, and parameters C₀, T₀, g, b and μ show sensitivity in CGND. Sensitivity analysis can be used to identify the most crucial disturbance parameters for various crystallization processes. This can guide the selection of the consideration of model errors and operating condition perturbations in robust optimization design.

Key words: sensitivity analysis, kinetic model, size distribution, population balance model, crystallization

摘要：

针对结晶模型中动力学模型参数和操作参数的不确定性，以间歇冷却结晶过程为研究对象，考虑了基于粒数衡算模型的三种简化结晶过程，评估了参数对产品晶体尺寸分布（CSD）和细晶形成的敏感性。在确保修正Morris筛选法和PAWN法收敛的情况下，分别定量分析了12个参数对晶体生长（CG）、晶体生长-成核（CGN）和晶体生长-成核-溶解（CGND）三种结晶过程模型有关产品指标的局部与全局敏感性，并进行了参数敏感性排序。结果表明，对于不同复杂度的模型情况，参数的敏感性有所不同。针对产品CSD，参数μ、C₀、b和m₀在CG和CGN中表现出显著敏感性，参数在CGND中不敏感；针对细晶，参数b、g和C₀在CGN中表现出显著敏感性，参数C₀、T₀、g、b和μ在CGND中表现出敏感性。通过敏感性分析法可以对不同结晶过程筛选出最重要的扰动参数，这将有助于指导鲁棒优化设计中选择需要考虑的模型误差和操作条件扰动。

关键词: 敏感性分析, 动力学模型, 粒度分布, 粒数衡算模型, 结晶

CLC Number:

TQ 028.5

Bin LIAN, Yan LONG, Qilei XU, Baoming SHAN, Xuezhong WANG, Fangkun ZHANG. Sensitivity analysis of model parameters and process operation for batch cooling crystallization process[J]. CIESC Journal, 2024, 75(12): 4587-4595.

连斌, 龙妍, 徐啟蕾, 单宝明, 王学重, 张方坤. 间歇冷却结晶过程模型参数及操作敏感性分析[J]. 化工学报, 2024, 75(12): 4587-4595.

Figures/Tables 8

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类型	参数	初始值
操作参数	晶种质量m₀	1.470 g
	晶种分布均值μ	127.780 μm
	晶种分布标准差σ	18.650
	溶液初始温度T₀	40℃
	溶液初始浓度C₀	0.104 g/g
	批次时间t_f	4600 s
动力学参数	生长模型系数k_g	8.5708 μm/s
	生长模型系数g	1.0000
	成核模型系数k_b	0.0380 μm^-3·s^-1
	成核模型系数b	3.4174
	溶解模型系数k_d	10.7192 μm/s
	溶解模型系数d	0.5122

类型	参数	初始值
操作参数	晶种质量m₀	1.470 g
	晶种分布均值μ	127.780 μm
	晶种分布标准差σ	18.650
	溶液初始温度T₀	40℃
	溶液初始浓度C₀	0.104 g/g
	批次时间t_f	4600 s
动力学参数	生长模型系数k_g	8.5708 μm/s
	生长模型系数g	1.0000
	成核模型系数k_b	0.0380 μm^-3·s^-1
	成核模型系数b	3.4174
	溶解模型系数k_d	10.7192 μm/s
	溶解模型系数d	0.5122

参数	CG	CGN		CGND
参数	F₁	F₁	F₂	F₁	F₂
μ	1.392	1.363	0.013	0.049	0.085
σ	0.108	0.109	0.007	0.025	0.002
m₀	0.241	0.235	0.010	0.023	0.027
C₀	0.912	0.893	0.128	0.014	1.450
T₀	0.002	0.002	0.001	0.028	0.827
t_f	0.012	0.012	0.024	0.015	0.073
k_g	0.013	0.013	0.034	0.033	0.069
g	0.070	0.073	0.192	0.043	0.414
k_b	—	0.001	0.009	0.021	0.010
b	—	0.005	0.217	0.019	0.211
k_d	—	—	—	0.011	0.017
d	—	—	—	0.016	0.054

参数	CG	CGN		CGND
参数	F₁	F₁	F₂	F₁	F₂
μ	1.392	1.363	0.013	0.049	0.085
σ	0.108	0.109	0.007	0.025	0.002
m₀	0.241	0.235	0.010	0.023	0.027
C₀	0.912	0.893	0.128	0.014	1.450
T₀	0.002	0.002	0.001	0.028	0.827
t_f	0.012	0.012	0.024	0.015	0.073
k_g	0.013	0.013	0.034	0.033	0.069
g	0.070	0.073	0.192	0.043	0.414
k_b	—	0.001	0.009	0.021	0.010
b	—	0.005	0.217	0.019	0.211
k_d	—	—	—	0.011	0.017
d	—	—	—	0.016	0.054

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