Mathematical modelling of water sorption isotherms and thermodynamic properties of municipal sewage sludge

doi:10.16085/j.issn.1000-6613.2021-0519

Abstract

Abstract:

The adsorption isotherms of municipal sludge at 30℃, 40℃, and 50℃ were determined by static gravimetric method. Eleven common mathematical models were selected to fit the experimental data, and the best model was analyzed. The thermodynamic properties of sludge were evaluated by net isosteric adsorption heat, differential entropy, diffusion pressure, net integral enthalpy and net integral entropy. The results showed that the isothermal curve belongs to type Ⅱ at constant temperature, the GAB model fitted well the isotherms data of sludge and was considered as the best model for predicting equilibrium moisture changes with water activity.Additionally, sorption isotherms data were used to determine the thermodynamic properties such as isosteric sorption heat, sorption entropy, spreading pressure, net integral enthalpy and entropy. Net isosteric heat of sorption and differential entropy were evaluated through direct use of moisture isotherms by applying the Clausius-Clapeyron equation and used to investigate the enthalpy-entropy compensation theory. The net isosteric adsorption heat and differential entropy decrease obviously with the increase of equilibrium water content. The harmonic mean temperature T_hm was not equal to the constant velocity temperature T_l, so the enthalpy-entropy compensation theory was established. The spreading pressure increased with the increase of water activity at a given temperature, and decreased with the increase of temperature at a given water activity. The net integral enthalpy decreased as the equilibrium moisture content increase. However, the net integral entropy decreased with the increase of equilibrium water content at low equilibrium water content, and reached the minimum values of -75.698J/(K?mol), -78.987 J/(K?mol) and -82.687 J/(K?mol) at 30℃, 40℃ and 50℃, respectively, and then increased.

Key words: municipal sewage sludge, adsorption, isotherms, model, thermodynamic properties

摘要：

采用静态重量法测定了市政污泥在30℃、40℃、50℃下的吸附等温线，选用11个常见的数学模型对实验数据进行了拟合并对最佳模型进行了解析，通过净等量吸附热q_st、微分熵ΔS、扩散压力π、净积分焓q_in和净积分熵ΔS_in等指标评价污泥的热力学性质。试验结果表明，在温度恒定时，等温曲线属于Ⅱ型，GAB模型拟合效果最佳，能较好地反映平衡含水量随水分活度的变化。应用Clausius-Clapeyron方程，利用等温线模型计算净等量吸附热和微分熵，随着平衡含水率的增加，净等量吸附热和微分熵明显降低，调和平均温度T_hm与等速温度T_l不等，焓-熵补偿理论成立。在一定的水活度下，扩散压力随温度的升高而减小，在温度恒定的情况下，扩张压力随水分活度增大而升高。净积分焓随平衡含水率的增加而减小，而净积分熵在低平衡含水率时随平衡含水率的增加而减小，在30℃、40℃和50℃时分别达到最小值-75.698J/(K?mol)、-78.987J/(K?mol)和-82.687J/(K?mol)，然后呈上升趋势。

关键词: 市政污泥, 吸附, 等温线, 模型, 热力学性质

CLC Number:

X705

GU Zhipan, YANG Jichun, ZHANG Ye, TAO Leren, LIU Fanhan. Mathematical modelling of water sorption isotherms and thermodynamic properties of municipal sewage sludge[J]. Chemical Industry and Engineering Progress, 2022, 41(2): 998-1008.

谷志攀, 阳季春, 张叶, 陶乐仁, 刘泛函. 市政污泥吸附等温线模型和热力学性质[J]. 化工进展, 2022, 41(2): 998-1008.

Figures/Tables 12

盐	水活性
盐	30℃	40℃	50℃
KOH	0.074	0.063	0.057
LiCl	0.11	0.11	0.11
MgCl₂	0.32	0.31	0.30
K₂CO₃	0.43	0.43	0.42
NaBr	0.56	0.53	0.51
NaNO₃	0.73	0.71	0.58
NaCl	0.75	0.75	0.71
KCl	0.84	0.82	0.77
BaCl₂	0.90	0.89	0.88

模型	函数表达式
Halsey	$M e = (- k l n ? a w) 1 n$
Henderson	$M e = - l n ? (1 - a w) a 1 b$
Oswin	$M e = k (a w 1 - a w) n$
Smith	$M e = a + b l n (1 - a w)$
Lespam	$M e = k 1 e k 2 a w t + b$
Modified Halsey	$a w = e - e (a + b t) M e c$
Modified Henderson	$a w = 1 - e [- a (t + b) M e c]$
Modified Oswin	$M e = (a + b t) (a w 1 - a w) n$
Enderby	$M e = (k 1 1 - n 1 a w + k 2 1 - n 2 a w) a w$
GAB	$M e = M m C K a w (1 - K a w) (1 - K a w + C K a w)$
Peleg	$M e = k 1 a w n 1 + k 2 a w n 2$

模型	函数表达式
Halsey	$M e = (- k l n ? a w) 1 n$
Henderson	$M e = - l n ? (1 - a w) a 1 b$
Oswin	$M e = k (a w 1 - a w) n$
Smith	$M e = a + b l n (1 - a w)$
Lespam	$M e = k 1 e k 2 a w t + b$
Modified Halsey	$a w = e - e (a + b t) M e c$
Modified Henderson	$a w = 1 - e [- a (t + b) M e c]$
Modified Oswin	$M e = (a + b t) (a w 1 - a w) n$
Enderby	$M e = (k 1 1 - n 1 a w + k 2 1 - n 2 a w) a w$
GAB	$M e = M m C K a w (1 - K a w) (1 - K a w + C K a w)$
Peleg	$M e = k 1 a w n 1 + k 2 a w n 2$

模型	参数	解吸			吸附
模型	参数	30℃	40℃	50℃	30℃	40℃	50℃
Enerby	k₁	164.6200	154.6625	97.5232	228.5969	67.6927	41.9163
	k₂	4.3777	4.1455	3.2694	4.1245	3.4799	2.8263
	n₁	-21.4747	-27.5731	-16.7879	-35.8708	-10.4499	-5.5114
	n₂	0.7922	0.8081	0.8657	0.8080	0.8355	0.8684
	R²	0.9987	0.9918	0.9914	0.9994	0.9992	0.9936
	SSE	6.7642×10^-5	2.2067×10^-5	2.2948×10^-4	5.3219×10^-5	5.7626×10^-5	1.8101×10^-4
GAB	M_m	6.9489	5.7250	4.9885	5.8989	5.5057	5.4636
	K	0.74617	0.78664	0.81484	0.7791	0.78411	0.77744
	C	38.6475	38.8496	30.2742	61.2461	19.2301	13.1561
	R²	0.9986	0.9993	0.9981	0.9996	0.9987	0.9979
	SSE	7.0842×10^-5	5.4423×10^-5	8.0862×10^-5	4.5813×10^-5	6.7642×10^-5	8.5269×10^-5
Henderson	a	0.004480	0.009660	0.01752	0.006690	0.01658	0.02156
	b	2.0713	1.8695	1.6997	1.9860	1.7112	1.6387
	R²	0.9834	0.9784	0.9784	0.9695	0.9915	0.9944
	SSE	6.6675×10^-4	1.0083×10^-3	1.0083×10^-3	1.6067×10^-3	2.2751×10^-4	1.6334×10^-4
Lespam	k₁	4.1040	2.7496	2.3542	1.8656	4.3583	6.6839
	k₂	87.0296	102.9505	109.1127	120.1665	82.3949	64.8542
	b	0.8122	1.31745	0.95785	3.09977	-1.5383	-4.6904
	R²	0.9871	0.9881	0.9789	0.9907	0.9812	0.9762
	SSE	4.2235×10^-4	3.5621×10^-4	9.7470×10^-4	2.4491×10^-4	8.2005×10^-4	1.1562×10^-3
Modified Halsey	a	11.6936	7.2225	7.8648	5.1827	10.5786	4.0135
	b	-1.50581	-0.67996	-0.92382	-0.11143	-1.51745	-0.03796
	c	2.3746	2.1245	2.0419	2.2667	2.0878	2.0452
	R²	0.9876	0.9906	0.9908	0.9964	0.9840	09864
	SSE	3.8973×10^-4	2.4711×10^-4	2.4270×10^-4	1.1932×10^-4	6.3179×10^-4	4.7042×10^-4
Modified Henderson	a	2.749×10^-5	7.2117×10^-5	8.4859×10^-5	3.92302×10^-5	9.31591×10^-5	1.12525×10^-4
	b	-153.8850	-197.6900	-157.8362	-155.6501	-160.9387	-160.8820
	c	2.1207	1.9468	1.8093	2.0644	1.7860	1.7145
	R²	0.9878	0.9831	0.9844	0.9738	0.9947	0.9958
	SSE	3.7629×10^-4	6.9230×10^-4	6.0489×10^-4	1.317×10^-3	1.5677×10^-4	1.3253×10^-4
Modified Oswin	a	-11.3030	-12.0411	-12.5870	-11.8017	-12.5025	-12.7686
	b	0.5534	0.5350	0.5216	0.5410	0.5235	0.5168
	n	0.3064	0.3387	0.3736	0.3181	0.3654	0.3854
	R²	0.9879	0.9980	0.9979	0.9955	0.9982	0.9933
	SSE	3.6957×10^-4	8.4066×10^-5	8.6269×10^-5	1.3914×10^-4	7.9659×10^-5	1.8762×10^-4
Peleg	k₁	13.9311	14.6001	15.3302	14.9750	13.2518	12.9026
	k₂	12.8412	10.8048	10.3439	10.6098	11.7910	12.5854
	n₁	4.5828	4.5950	5.3950	4.4285	5.6993	7.0189
	n₂	0.3601	0.3618	0.4305	0.2973	0.5238	0.6412
	R²	0.9899	0.9988	0.9978	0.9983	0.9980	0.9899
	SSE	2.6253×10^-4	6.6439×10^-5	8.8472×10^-5	7.7456×10^-5	8.4066×10^-5	2.3509×10^-4
Halsey	k	458.71	87.4532	53.1284	159.9017	62.3501	77.6911
	n	2.7239	2.23048	2.0917	2.4367	2.1552	2.2392
	R²	0.9890	0.9850	0.9930	0.9890	0.9768	0.9818
	SSE	5.8658×10^-4	8.0070×10^-4	3.7246×10^-4	5.865×10^-4	1.239×10^-3	9.7199×10^-4
Oswin	k	11.37929	9.2118	8.3955	9.7888	8.4931	8.6816
	n	0.2821	0.3469	0.3676	0.3189	0.3608	0.3410
	R²	0.9942	0.9985	0.9965	0.9954	0.9972	0.9980
	SSE	3.0823×10^-4	7.8053×10^-5	1.8511×10^-4	2.4399×10^-4	1.4764×10^-4	1.0481×10^-4
Smith	a	6.1447	3.9708	3.4089	4.7343	3.4131	3.7764
	b	-6.6351	-6.8745	-6.6602	-6.5677	-6.6802	-6.3820
	R²	0.9946	0.9942	0.9987	0.9967	0.9902	0.9906
	SSE	2.8681×10^-4	3.0823×10^-4	6.7347×10^-4	1.7440×10^-4	5.2348×10^-4	5.0093×10^-4

模型	参数	解吸			吸附
模型	参数	30℃	40℃	50℃	30℃	40℃	50℃
Enerby	k₁	164.6200	154.6625	97.5232	228.5969	67.6927	41.9163
	k₂	4.3777	4.1455	3.2694	4.1245	3.4799	2.8263
	n₁	-21.4747	-27.5731	-16.7879	-35.8708	-10.4499	-5.5114
	n₂	0.7922	0.8081	0.8657	0.8080	0.8355	0.8684
	R²	0.9987	0.9918	0.9914	0.9994	0.9992	0.9936
	SSE	6.7642×10^-5	2.2067×10^-5	2.2948×10^-4	5.3219×10^-5	5.7626×10^-5	1.8101×10^-4
GAB	M_m	6.9489	5.7250	4.9885	5.8989	5.5057	5.4636
	K	0.74617	0.78664	0.81484	0.7791	0.78411	0.77744
	C	38.6475	38.8496	30.2742	61.2461	19.2301	13.1561
	R²	0.9986	0.9993	0.9981	0.9996	0.9987	0.9979
	SSE	7.0842×10^-5	5.4423×10^-5	8.0862×10^-5	4.5813×10^-5	6.7642×10^-5	8.5269×10^-5
Henderson	a	0.004480	0.009660	0.01752	0.006690	0.01658	0.02156
	b	2.0713	1.8695	1.6997	1.9860	1.7112	1.6387
	R²	0.9834	0.9784	0.9784	0.9695	0.9915	0.9944
	SSE	6.6675×10^-4	1.0083×10^-3	1.0083×10^-3	1.6067×10^-3	2.2751×10^-4	1.6334×10^-4
Lespam	k₁	4.1040	2.7496	2.3542	1.8656	4.3583	6.6839
	k₂	87.0296	102.9505	109.1127	120.1665	82.3949	64.8542
	b	0.8122	1.31745	0.95785	3.09977	-1.5383	-4.6904
	R²	0.9871	0.9881	0.9789	0.9907	0.9812	0.9762
	SSE	4.2235×10^-4	3.5621×10^-4	9.7470×10^-4	2.4491×10^-4	8.2005×10^-4	1.1562×10^-3
Modified Halsey	a	11.6936	7.2225	7.8648	5.1827	10.5786	4.0135
	b	-1.50581	-0.67996	-0.92382	-0.11143	-1.51745	-0.03796
	c	2.3746	2.1245	2.0419	2.2667	2.0878	2.0452
	R²	0.9876	0.9906	0.9908	0.9964	0.9840	09864
	SSE	3.8973×10^-4	2.4711×10^-4	2.4270×10^-4	1.1932×10^-4	6.3179×10^-4	4.7042×10^-4
Modified Henderson	a	2.749×10^-5	7.2117×10^-5	8.4859×10^-5	3.92302×10^-5	9.31591×10^-5	1.12525×10^-4
	b	-153.8850	-197.6900	-157.8362	-155.6501	-160.9387	-160.8820
	c	2.1207	1.9468	1.8093	2.0644	1.7860	1.7145
	R²	0.9878	0.9831	0.9844	0.9738	0.9947	0.9958
	SSE	3.7629×10^-4	6.9230×10^-4	6.0489×10^-4	1.317×10^-3	1.5677×10^-4	1.3253×10^-4
Modified Oswin	a	-11.3030	-12.0411	-12.5870	-11.8017	-12.5025	-12.7686
	b	0.5534	0.5350	0.5216	0.5410	0.5235	0.5168
	n	0.3064	0.3387	0.3736	0.3181	0.3654	0.3854
	R²	0.9879	0.9980	0.9979	0.9955	0.9982	0.9933
	SSE	3.6957×10^-4	8.4066×10^-5	8.6269×10^-5	1.3914×10^-4	7.9659×10^-5	1.8762×10^-4
Peleg	k₁	13.9311	14.6001	15.3302	14.9750	13.2518	12.9026
	k₂	12.8412	10.8048	10.3439	10.6098	11.7910	12.5854
	n₁	4.5828	4.5950	5.3950	4.4285	5.6993	7.0189
	n₂	0.3601	0.3618	0.4305	0.2973	0.5238	0.6412
	R²	0.9899	0.9988	0.9978	0.9983	0.9980	0.9899
	SSE	2.6253×10^-4	6.6439×10^-5	8.8472×10^-5	7.7456×10^-5	8.4066×10^-5	2.3509×10^-4
Halsey	k	458.71	87.4532	53.1284	159.9017	62.3501	77.6911
	n	2.7239	2.23048	2.0917	2.4367	2.1552	2.2392
	R²	0.9890	0.9850	0.9930	0.9890	0.9768	0.9818
	SSE	5.8658×10^-4	8.0070×10^-4	3.7246×10^-4	5.865×10^-4	1.239×10^-3	9.7199×10^-4
Oswin	k	11.37929	9.2118	8.3955	9.7888	8.4931	8.6816
	n	0.2821	0.3469	0.3676	0.3189	0.3608	0.3410
	R²	0.9942	0.9985	0.9965	0.9954	0.9972	0.9980
	SSE	3.0823×10^-4	7.8053×10^-5	1.8511×10^-4	2.4399×10^-4	1.4764×10^-4	1.0481×10^-4
Smith	a	6.1447	3.9708	3.4089	4.7343	3.4131	3.7764
	b	-6.6351	-6.8745	-6.6602	-6.5677	-6.6802	-6.3820
	R²	0.9946	0.9942	0.9987	0.9967	0.9902	0.9906
	SSE	2.8681×10^-4	3.0823×10^-4	6.7347×10^-4	1.7440×10^-4	5.2348×10^-4	5.0093×10^-4

参数	吸附	解吸
M_m0	0.02996	1.6379
C₀	1.1321	2.5146×10^-12
K₀	3.0870	0.7566
ΔH/kJ·mol^-1	13.7074	3.2062
H_M-H_N/kJ·mol^-1	8.9807	77.6208
H_L-H_N/kJ·mol^-1	-3.5705	0.07985

References 40

1	MOU X Z, CHEN Z Q. Experimental study on the effect of sludge thickness on the characteristics of ultrasound-assisted hot air convective drying municipal sewage sludge[J]. Drying Technology, 2021, 39(6): 752-764.
2	陈思思, 杨殿海, 庞维海, 等. 我国剩余污泥厌氧转化的主要影响因素及影响机制研究进展[J]. 化工进展, 2020, 39(4): 1511-1520.
	CHEN Sisi, YANG Dianhai, PANG Weihai, et al. Main influencing factors and mechanisms of anaerobic transformation of excess sludge in China[J]. Chemical Industry and Engineering Progress, 2020, 39(4): 1511-1520.
3	ERIKSSON E, CHRISTENSEN N, EJBYE SCHMIDT J, et al. Potential priority pollutants in sewage sludge[J]. Desalination, 2008, 226(1/2/3): 371-388.
4	宋文婷, 郭静, 杨倩倩, 等. 污泥有机污染物降解研究进展[J]. 化工进展, 2020, 39(1): 380-386.
	SONG Wenting, GUO Jing, YANG Qianqian, et al. Research progress on degradation of sludge organic pollutants[J]. Chemical Industry and Engineering Progress, 2020, 39(1): 380-386.
5	张俊杰, 邵敬爱, 黄河洵, 等. 利用污泥制备活性炭及其吸附特性的研究进展[J]. 化工进展, 2017, 36(10): 3876-3886.
	ZHANG Junjie, SHAO Jing’ai, HUANG Hexun, et al. Review on the preparation of activated carbon from sludge and its adsorption characteristics[J]. Chemical Industry and Engineering Progress, 2017, 36(10): 3876-3886.
6	陈丹丹, 窦昱昊, 卢平, 等. 污泥深度脱水技术研究进展[J]. 化工进展, 2019, 38(10): 4722-4746.
	CHEN Dandan, DOU Yuhao, LU Ping, et al. A review on sludge deep dewatering technology[J]. Chemical Industry and Engineering Progress, 2019, 38(10): 4722-4746.
7	米琼, 戴世金, 张瑞娜, 等. 干污泥高维填埋的堆体边坡稳定性模拟与分析[J]. 中国环境科学, 2018, 38(4): 1397-1402.
	MI Qiong, DAI Shijin, ZHANG Ruina, et al. Slope stability simulation of dry sludge pile in high-dimensional landfill operation[J]. China Environmental Science, 2018, 38(4): 1397-1402.
8	王子文, 曹蓉, 杨艳坤, 等. 聚季铵盐调理污泥深度脱水过程与中试效能[J]. 化工进展, 2019, 38(7): 3458-3464.
	WANG Ziwen, CAO Rong, YANG Yankun, et al. Performance and pilot-scale efficiency of polyquaternary ammonium in sludge deep dewatering process[J]. Chemical Industry and Engineering Progress, 2019, 38(7): 3458-3464.
9	WU B R, DAI X H, CHAI X L. Critical review on dewatering of sewage sludge: Influential mechanism, conditioning technologies and implications to sludge re-utilizations[J]. Water Research, 2020, 180: 115912.
10	SYED-HASSAN S S A, WANG Y, HU S, et al. Thermochemical processing of sewage sludge to energy and fuel: fundamentals, challenges and considerations[J]. Renewable and Sustainable Energy Reviews, 2017, 80: 888-913.
11	CHAN W P, WANG J Y. Comprehensive characterisation of sewage sludge for thermochemical conversion processes—Based on Singapore survey[J]. Waste Management, 2016, 54: 131-142.
12	郑晓园, 蒋正伟, 陈伟, 等. 污水污泥水热炭化过程中磷的迁移转化特性[J]. 化工进展, 2020, 39(5): 2017-2025.
	ZHENG Xiaoyuan, JIANG Zhengwei, CHEN Wei, et al. Migration and transformation of phosphorus in sewage sludge during hydrothermal carbonization process[J]. Chemical Industry and Engineering Progress, 2020, 39(5): 2017-2025.
13	范海宏, 武亚磊, 李斌斌, 等. 市政污泥干化动力学研究[J]. 环境工程学报, 2015, 9(9): 4488-4494.
	FAN Haihong, WU Yalei, LI Binbin, et al. Investigation of drying kinetic of municipal dewater sewage sludge[J]. Chinese Journal of Environmental Engineering, 2015, 9(9): 4488-4494.
14	张绪坤, 刘胜平, 吴青荣, 等. 污泥低温干燥动力学特性及干燥参数优化[J]. 农业工程学报, 2017, 33(17): 216-223.
	ZHANG Xukun, LIU Shengping, WU Qingrong, et al. Drying kinetics and parameters optimization of sludge drying at low temperature[J]. Transactions of the Chinese Society of Agricultural Engineering, 2017, 33(17): 216-223.
15	李斌斌, 范海宏, 任洋明, 等. 城市污泥薄层干燥特性及动力学研究[J]. 环境工程, 2016, 34(10): 103-107.
	LI Binbin, FAN Haihong, REN Yangming, et al. Municipal sludge drying characteristics and dynamics based on thin layer drying model[J]. Environmental Engineering, 2016, 34(10): 103-107.
16	郑龙, 伍健东, 周兴求, 等. 温度和相对湿度对污泥低温干燥速率的影响[J]. 环境工程学报, 2016, 10(2): 922-928.
	ZHENG Long, WU Jiandong, ZHOU Xingqiu, et al. Effects of temperature and relative humidity on drying rate of sludge at low temperature[J]. Chinese Journal of Environmental Engineering, 2016, 10(2): 922-928.
17	邓文义, 梅静, 刘亚军, 等. CaO和木屑对市政污泥干化过程中黏滞特性的影响[J]. 化工进展, 2017, 36(5): 1933-1939.
	DENG Wenyi, MEI Jing, LIU Yajun, et al. Effect of CaO and sawdust on sticky properties of municipal sewage sludge during drying process[J]. Chemical Industry and Engineering Progress, 2017, 36(5): 1933-1939.
18	刘亚军, 王爱春, 邓文义. 市政污泥热力干化过程中黏滞特性研究进展[J]. 化工进展, 2018, 37(6): 2378-2385.
	LIU Yajun, WANG Aichun, DENG Wenyi. Progress in sticky characteristics of sewage sludge during thermal drying process[J]. Chemical Industry and Engineering Progress, 2018, 37(6): 2378-2385.
19	郑玲玲, 程榕, 郑燕萍, 等. MVR空心桨叶干燥污泥的特性及动力学[J]. 化工进展, 2016, 35(S1): 53-57.
	ZHENG Lingling, CHENG Rong, ZHENG Yanping, et al. Drying properties and kinetics of MVR technology applied to the hollow blade dryer drying sludge[J]. Chemical Industry and Engineering Progress, 2016, 35(S1): 53-57.
20	LÉONARD A, BLACHER S, MARCHOT P, et al. Measurement of shrinkage and cracks associated to convective drying of soft materials by X-ray microtomography[J]. Drying Technology, 2004, 22(7): 1695-1708.
21	FONT R, GOMEZ-RICO M F, FULLANA A. Skin effect in the heat and mass transfer model for sewage sludge drying[J]. Separation and Purification Technology, 2011, 77(1): 146-161.
22	HUANG Y W, CHEN M Q. Thin-layer isothermal drying kinetics of municipal sewage sludge based on two falling rate stages during hot-air-forced convection[J]. Journal of Thermal Analysis and Calorimetry, 2017, 129(1): 567-575.
23	GUO J, CHEN M Q, HUANG Y W, et al. Salinity effects on ultrasound-assisted hot air drying kinetics of sewage sludge[J]. Thermochimica Acta, 2019, 678: 178298.
24	EOM H, JANG Y H, LEE D Y, et al. Optimization of a hybrid sludge drying system with flush drying and microwave drying technology[J]. Chemical Engineering Research and Design, 2019, 148: 68-74.
25	DI FRAIA S, FIGAJ R D, MASSAROTTI N, et al. An integrated system for sewage sludge drying through solar energy and a combined heat and power unit fuelled by biogas[J]. Energy Conversion and Management, 2018, 171: 587-603.
26	WANG P L, MOHAMMED D, ZHOU P, et al. Roof solar drying processes for sewage sludge within sandwich-like chamber bed[J]. Renewable Energy, 2019, 136: 1071-1081.
27	HASSINE N BEN, CHESNEAU X, LAATAR A H, et al. Modelisation and simulation of heat and mass transfers during solar drying of sewage sludge with introduction of real climatic conditions[J]. Journal of Applied Fluid Mechanics, 2017, 10(2): 651-659.
28	JIANG J, DANG L P, YUENSIN C, et al. Simulation of microwave thin layer drying process by a new theoretical model[J]. Chemical Engineering Science, 2017, 162: 69-76.
29	BELLUR S R, CORONELLA C J, VÁSQUEZ V R. Analysis of biosolids equilibrium moisture and drying[J]. Environmental Progress & Sustainable Energy, 2009, 28(2): 291-298.
30	REMINGTON C, BOURGAULT C, DOREA C C. Measurement and modelling of moisture sorption isotherm and heat of sorption of fresh feces[J]. Water, 2020, 12(2): 323.
31	BOUGAYR E H, LAKHAL E K, IDLIMAM A, et al. Experimental study of hygroscopic equilibrium and thermodynamic properties of sewage sludge[J]. Applied Thermal Engineering, 2018, 143: 521-531.
32	FAKHFAKH R, MIHOUBI D, KECHAOU N. Moisture sorption isotherms and thermodynamic properties of bovine leather[J]. Heat and Mass Transfer, 2018, 54(4): 1163-1176.
33	杨昭, 李想, 陶志超. 豌豆种子吸附等温线与热力学性质研究[J]. 农业机械学报, 2017, 48(10): 323-329.
	YANG Zhao, LI Xiang, TAO Zhichao. Sorption isotherms and thermodynamic properties of pea seed[J]. Transactions of the Chinese Society for Agricultural Machinery, 2017, 48(10): 323-329.
34	NOURHÈNE B, NEILA B, MOHAMMED K, et al. Sorptions isotherms and isosteric heats of sorption of olive leaves (Chemlali variety): experimental and mathematical investigations[J]. Food and Bioproducts Processing, 2008, 86(3): 167-175.
35	BERTOLIN C, DE FERRI L, STROJECKI M. Application of the Guggenheim, Anderson, de Boer (GAB) equation to sealing treatments on pine wood[J]. Procedia Structural Integrity, 2020, 26: 147-154.
36	POLATOĞLU B, BEŞE A V, KAYA M, et al. Moisture adsorption isotherms and thermodynamics properties of sucuk (Turkish dry-fermented sausage)[J]. Food and Bioproducts Processing, 2011, 89(4): 449-456.
37	MGHAZLI S, IDLIMAM A, MAHROUZ M, et al. Comparative moisture sorption isotherms, modelling and isosteric heat of sorption of controlled and irradiated Moroccan rosemary leaves[J]. Industrial Crops and Products, 2016, 88: 28-35.
38	OUERTANI S, AZZOUZ S, HASSINI L, et al. Moisture sorption isotherms and thermodynamic properties of Jack pine and palm wood: comparative study[J]. Industrial Crops and Products, 2014, 56: 200-210.
39	IGLESIAS H A, CHIRIFE J. Prediction of the effect of temperature on water sorption isotherms of food material[J]. International Journal of Food Science & Technology, 1976, 11(2): 109-116.
40	KAYA S, KAHYAOGLU T. Moisture sorption and thermodynamic properties of safflower petals and tarragon[J]. Journal of Food Engineering, 2007, 78(2): 413-421.

[1]	XU Chenyang, DU Jian, ZHANG Lei. Chemical reaction evaluation based on graph network [J]. Chemical Industry and Engineering Progress, 2023, 42(S1): 205-212.
[2]	WANG Shengyan, DENG Shuai, ZHAO Ruikai. Research progress on carbon dioxide capture technology based on electric swing adsorption [J]. Chemical Industry and Engineering Progress, 2023, 42(S1): 233-245.
[3]	CUI Shoucheng, XU Hongbo, PENG Nan. Simulation analysis of two MOFs materials for O₂/He adsorption separation [J]. Chemical Industry and Engineering Progress, 2023, 42(S1): 382-390.
[4]	CHEN Chongming, CHEN Qiu, GONG Yunqian, CHE Kai, YU Jinxing, SUN Nannan. Research progresses on zeolite-based CO₂ adsorbents [J]. Chemical Industry and Engineering Progress, 2023, 42(S1): 411-419.
[5]	XU Chunshu, YAO Qingda, LIANG Yongxian, ZHOU Hualong. Research progress on functionalization strategies of covalent organic frame materials and its adsorption properties for Hg(Ⅱ) and Cr(Ⅵ) [J]. Chemical Industry and Engineering Progress, 2023, 42(S1): 461-478.
[6]	GU Yongzheng, ZHANG Yongsheng. Dynamic behavior and kinetic model of Hg⁰ adsorption by HBr-modified fly ash [J]. Chemical Industry and Engineering Progress, 2023, 42(S1): 498-509.
[7]	GUO Qiang, ZHAO Wenkai, XIAO Yonghou. Numerical simulation of enhancing fluid perturbation to improve separation of dimethyl sulfide/nitrogen via pressure swing adsorption [J]. Chemical Industry and Engineering Progress, 2023, 42(S1): 64-72.
[8]	ZHANG Fan, TAO Shaohui, CHEN Yushi, XIANG Shuguang. Initializing distillation column simulation based on the improved constant heat transport model [J]. Chemical Industry and Engineering Progress, 2023, 42(9): 4550-4558.
[9]	GE Yafen, SUN Yu, XIAO Peng, LIU Qi, LIU Bo, SUN Chengying, GONG Yanjun. Research progress of zeolite for VOCs removal [J]. Chemical Industry and Engineering Progress, 2023, 42(9): 4716-4730.
[10]	YANG Ying, HOU Haojie, HUANG Rui, CUI Yu, WANG Bing, LIU Jian, BAO Weiren, CHANG Liping, WANG Jiancheng, HAN Lina. Coal tar phenol-based carbon nanosphere prepared by Stöber method for adsorption of CO₂ [J]. Chemical Industry and Engineering Progress, 2023, 42(9): 5011-5018.
[11]	WU Zhenghao, ZHOU Tianhang, LAN Xingying, XU Chunming. AI-driven innovative design of chemicals in practice and perspective [J]. Chemical Industry and Engineering Progress, 2023, 42(8): 3910-3916.
[12]	ZHANG Zhichen, ZHU Yunfeng, CHENG Weishu, MA Shoutao, JIANG Jie, SUN Bing, ZHOU Zichen, XU Wei. Research advances on runaway decomposition of high pressure polyethylene: Reaction mechanism, initiation system and model [J]. Chemical Industry and Engineering Progress, 2023, 42(8): 3979-3989.
[13]	JIANG Jing, CHEN Xiaoyu, ZHANG Ruiyan, SHENG Guangyao. Research progress of manganese-loaded biochar preparation and its application in environmental remediation [J]. Chemical Industry and Engineering Progress, 2023, 42(8): 4385-4397.
[14]	ZHANG Zhen, LI Dan, CHEN Chen, WU Jinglan, YING Hanjie, QIAO Hao. Separation and purification of salivary acids with adsorption resin [J]. Chemical Industry and Engineering Progress, 2023, 42(8): 4153-4158.
[15]	WANG Zhicai, LIU Weiwei, ZHOU Cong, PAN Chunxiu, YAN Honglei, LI Zhanku, YAN Jingchong, REN Shibiao, LEI Zhiping, SHUI Hengfu. Synthesis and performance of a superplasticizer based on coal-based humic acid [J]. Chemical Industry and Engineering Progress, 2023, 42(7): 3634-3642.