Surrogate modeling and optimization of wet phosphoric acid production process based on mechanism and data hybrid driven

doi:10.11949/0438-1157.20231290

Abstract

Abstract:

Based on Aspen Plus platform and combined with the dynamic subroutine of acid decomposition reaction and crystallization kinetics of phosphate rock written by Fortran, the rigorous mechanism modeling of the whole hemi-dihydrate wet phosphoric acid process was completed, and the model was calibrated with industrial data. Quasi-Monte Carlo stochastic simulation was then used to generate a high-quality sample data set, and a machine learning algorithm was used to establish an agent model of the phosphoric acid production process. The results show that the surrogate model obtained by this method can accurately predict the key parameters of phosphoric acid production process. For example, the prediction accuracy of random forest agent model is the best in this case, most of the relative errors are controlled within 2.5%, and the maximum is not more than 10%. Based on this surrogate model, the operating parameters of the production process were optimized. The results showed that under the condition that the lower limit of P₂O₅ concentration in the finished phosphoric acid was 37%, and the upper limit of $S O 4 2 -$ concentration was 5%, the maximum phosphorus yield could be obtained by 98%, and the optimization effect was obvious, and the technical production index was met. It can provide solutions and data support for real-time optimization operation, design and transformation of production.

Key words: wet phosphoric acid, Aspen Plus process simulation, user dynamics model, machine learning, surrogate model, optimization

摘要：

基于Aspen Plus平台，结合Fortran编制的磷矿酸解反应和结晶动力学模型子程序完成了整个半水-二水湿法磷酸工艺流程的严格机理建模，并用工业数据进行了模型的校正；然后采用拟Monte Carlo随机模拟产生高质量样本数据集，并用机器学习算法建立了磷酸生产过程代理模型。结果表明，通过本方法获得的代理模型可实现磷酸生产过程关键参数的准确预测，如案例中随机森林代理模型的预测性能最好，大部分误差控制在2.5%以内，最大不超过10%。基于此代理模型，对生产过程的操作参数进行了优化计算，结果表明在成品磷酸P₂O₅浓度下限为37%， $S O 4 2 -$ 浓度上限为5%的约束条件下，可获得最大磷收率98%，优化效果明显，且满足技术生产指标，可为生产的实时优化操作与设计改造提供方案和数据支持。

关键词: 湿法磷酸, Aspen Plus流程模拟, 用户动力学模型, 机器学习, 代理模型, 优化

CLC Number:

TQ 126.3

Yujiao ZENG, Xin XIAO, Gang YANG, Yibo ZHANG, Guangming ZHENG, Fang LI, Fengling WANG. Surrogate modeling and optimization of wet phosphoric acid production process based on mechanism and data hybrid driven[J]. CIESC Journal, 2024, 75(3): 936-944.

曾玉娇, 肖炘, 杨刚, 张意博, 郑光明, 李防, 汪凤玲. 基于机理与数据混合驱动的湿法磷酸生产过程代理建模与优化[J]. 化工学报, 2024, 75(3): 936-944.

Figures/Tables 12

Fig.1 Schematic diagram of hemi-dihydrate wet phosphoric acid process in an enterprise

Fig.2 Effect of temperature on leaching rate of phosphate rock

Table 1 Comparison of fitting performance of three dynamic models

性能指标	液膜扩散控制	表面化学反应	固膜扩散控制
R²最小值	0.8996	0.9294	0.9776
R²平均值	0.9112	0.9656	0.9881
R²最大值	0.9223	0.9771	0.9907

Fig.3 Aspen Plus simulation flow chart of hemi-dihydrate phosphoric acid process

Table 2 Comparison between simulated and actual values of Aspen Plus

流股	参数	模拟结果	工厂数据	误差/%
成品酸	质量流量	138.35 t/h	136.05 t/h	1.69
	P₂O₅含量	39.16%	40%	2.10
	SO $4 2 -$ 含量	4.31%	4%	7.75
半水返酸	质量流量	414.37 t/h	384 t/h	7.91
	P₂O₅含量	32.19%	34%	5.32
	SO $4 2 -$ 含量	3.17%	3%	5.67
二水料浆	质量流量	797.46 t/h	760.2 t/h	4.90
	P₂O₅含量	12.03%	11%	9.36
	SO $4 2 -$ 含量	4.47%	5%	10.60
二水石膏	质量流量	376.95 t/h	370 t/h	1.88
	P₂O₅含量	0.68%	0.75%	9.33
	CaSO₄含量	88%	92%	4.35
	含液量	16.55%	18%	8.06

Table 2 Comparison between simulated and actual values of Aspen Plus

流股	参数	模拟结果	工厂数据	误差/%
成品酸	质量流量	138.35 t/h	136.05 t/h	1.69
	P₂O₅含量	39.16%	40%	2.10
	SO $4 2 -$ 含量	4.31%	4%	7.75
半水返酸	质量流量	414.37 t/h	384 t/h	7.91
	P₂O₅含量	32.19%	34%	5.32
	SO $4 2 -$ 含量	3.17%	3%	5.67
二水料浆	质量流量	797.46 t/h	760.2 t/h	4.90
	P₂O₅含量	12.03%	11%	9.36
	SO $4 2 -$ 含量	4.47%	5%	10.60
二水石膏	质量流量	376.95 t/h	370 t/h	1.88
	P₂O₅含量	0.68%	0.75%	9.33
	CaSO₄含量	88%	92%	4.35
	含液量	16.55%	18%	8.06

Fig.4 Comparison between predicted and actual values of SVR model

Fig.5 Predicted relative error values of SVR model

Fig.6 Predicted relative error values of ANN model

Fig.7 Predicted relative error values of RF model

Table 3 Performance evaluation of surrogate models on the training and testing sets

模型	训练集			测试集
模型	MAE	RMSE	R²	MAE	RMSE	R²
SVR	0.1754	0.5771	0.9868	0.2689	0.6854	0.9758
ANN	0.7821	0.9406	0.9172	0.7636	0.9281	0.8957
RF	0.1523	0.1369	0.9982	0.1678	0.1773	0.9964

Table 4 Optimization results of decision variables under the objective of maximizing phosphorus yield

变量	参数名称	波动范围	基础案例	优化方案
X₁	F_in，sa/(kg/h)	90~120	90	112
X₂	β₁	1~6	1	2.6
X₃	β₂	1~6	1	1.3
X₄	ΔT₁/℃	2~20	10	12
X₅	β₃	1~6	1	1.4
X₆	ΔT₂/℃	2~20	10	10
X₇	F_in，wa/(kg/h)	80~160	90	100
成品酸中P₂O₅含量/%			38	37.5
成品酸SO $4 2 -$ 含量/%			4	4.31
成品酸质量流量/（kg/h）			112	115.09
磷收率/%			86.7	98.51

Table 4 Optimization results of decision variables under the objective of maximizing phosphorus yield

变量	参数名称	波动范围	基础案例	优化方案
X₁	F_in，sa/(kg/h)	90~120	90	112
X₂	β₁	1~6	1	2.6
X₃	β₂	1~6	1	1.3
X₄	ΔT₁/℃	2~20	10	12
X₅	β₃	1~6	1	1.4
X₆	ΔT₂/℃	2~20	10	10
X₇	F_in，wa/(kg/h)	80~160	90	100
成品酸中P₂O₅含量/%			38	37.5
成品酸SO $4 2 -$ 含量/%			4	4.31
成品酸质量流量/（kg/h）			112	115.09
磷收率/%			86.7	98.51

Table 5 Comparison of optimization results of three product schemes

变量	参数名称	波动范围	方案1	方案2	方案3
X₁	F_in，sa/(kg/h)	90~120	112	113.27	94.05
X₂	β₁	1~6	2.6	3.1	1.645
X₃	β₂	1~6	1.3	2.73	1.4
X₄	ΔT₁/℃	1~20	12	15	10
X₅	β₃	1~6	1.4	2.1	1.8
X₆	ΔT₂/℃	2~20	10	12	10
X₇	F_in，wa/(kg/h)	80~160	100	110	105
成品酸中P₂O₅浓度/%			37.5	40.56	39.76
成品酸中SO $4 2 -$ 浓度/%			4.31	4.98	3.98
成品酸质量流量/（kg/h）			115.09	110.24	112.21
磷收率/%			98. 51	98.76	96.71

Table 5 Comparison of optimization results of three product schemes

变量	参数名称	波动范围	方案1	方案2	方案3
X₁	F_in，sa/(kg/h)	90~120	112	113.27	94.05
X₂	β₁	1~6	2.6	3.1	1.645
X₃	β₂	1~6	1.3	2.73	1.4
X₄	ΔT₁/℃	1~20	12	15	10
X₅	β₃	1~6	1.4	2.1	1.8
X₆	ΔT₂/℃	2~20	10	12	10
X₇	F_in，wa/(kg/h)	80~160	100	110	105
成品酸中P₂O₅浓度/%			37.5	40.56	39.76
成品酸中SO $4 2 -$ 浓度/%			4.31	4.98	3.98
成品酸质量流量/（kg/h）			115.09	110.24	112.21
磷收率/%			98. 51	98.76	96.71

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