市政污泥吸附等温线模型和热力学性质

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

化工进展 ›› 2022, Vol. 41 ›› Issue (2): 998-1008.DOI: 10.16085/j.issn.1000-6613.2021-0519

市政污泥吸附等温线模型和热力学性质

谷志攀¹^,²(), 阳季春², 张叶², 陶乐仁¹^,³(), 刘泛函²

^1.上海理工大学能源与动力工程学院制冷与低温研究所，上海 200093
^2.嘉兴学院建筑工程学院，浙江嘉兴 314001
^3.上海市动力工程多相流动与传热重点实验室，上海 200093

收稿日期:2021-03-15 修回日期:2021-05-23 出版日期:2022-02-05 发布日期:2022-02-23
通讯作者: 陶乐仁
作者简介:谷志攀（1983—），男，讲师，博士研究生，研究方向为多孔介质传热传质。E-mail：guzhipan418@126.com。
基金资助:
国家自然科学基金(51568060);浙江省自然科学基金青年科学基金(LQ19E080014);浙江省基础公益研究计划(LGG19E060005);上海市动力工程多相流动与传热重点实验室项目(1N-15-301-101)

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

GU Zhipan¹^,²(), YANG Jichun², ZHANG Ye², TAO Leren¹^,³(), LIU Fanhan²

^1.Instiute of Refrigeration and Cryogenics, School of Energy and Power, University of Shanghai for Science and Technology, Shanghai 200093, China
^2.School of Architecture and Civil Engineering, Jiaxing University, Jiaxing 314001, Zhejiang, China
^3.Shanghai Key Laboratory of Multiphase Flow and Heat Transfer in Power Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China

Received:2021-03-15 Revised:2021-05-23 Online:2022-02-05 Published:2022-02-23
Contact: TAO Leren

摘要/Abstract

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

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

中图分类号:

X705

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.

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.

图/表 12

表1 饱和盐溶液及其相应的水活性

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

表2 等温线模型

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	$M e = k 1 a w n 1 + k 2 a w n 2$

表2 等温线模型

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	$M e = k 1 a w n 1 + k 2 a w n 2$

图1 平衡含水率Me随水分活度aw的变化

表3 污泥3吸附、解吸等温线模型参数及精度

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

表3 污泥3吸附、解吸等温线模型参数及精度

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

图2 污泥吸附和解吸等温线的GAB模型拟合

表4 GAB模型参数

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

图3 污泥净等量吸附热qst随平衡含水率Me的变化曲线

图4 污泥微分熵ΔS随平衡含水率Me的变化曲线

图5 污泥净等量吸附热qst与微分熵ΔS焓熵补偿理论拟合曲线

图6 不同温度下扩张压力曲线

图7 污泥净积分焓qin随平衡含水量Me变化曲线

图8 净积分熵ΔSin随平衡含水量Me变化曲线

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市政污泥吸附等温线模型和热力学性质

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

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