典型吸附模型的非线性和线性拟合对比分析
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摘要
为了验证各种典型吸附模型在非线性拟合和线性拟合的条件下,拟合结果是否相同这一问题,文章以沙粒对氨氮的吸附试验为例,对Langmuir和Freundlish吸附等温线模型以及准一级和准二级吸附动力学模型和附热力学Van’t Hoff模型进行了相同试验数据条件下的非线性拟合和线性拟合。结果表明,两种吸附等温线模型和准一级动力学模型的线性拟合相关系数小于对应的非线性拟合相关系数,并且两种拟合所得参数的差距也较大;但是,在准二级吸附动力学模型和Van’t Hoff模型中,情况又有所不同,表现出来线性拟合的相关系数大于等于非线性拟合的相关系数,并且两种拟合所得参数的相对误差小于1%,因此,可将其作为判定线性拟合结果是否合理的一个参考依据。综上所述,吸附模型的拟合应尽量采用非线性拟合,如若采用线性拟合,则有可能会带来较大的误差,从而影响吸附模型的精度。
In order to verify whether the fitting results were same by nonlinear fitting and linear fitting about various typical adsorption models,the paper took the experiment of sand adsorbing ammonia nitrogen.The Langmuir and Freundlish adsorption isotherm models,pseudo-first-order and pseudo-second-order adsorption kinetics models and Van't Hoff model of adsorption thermodynamics were fitted by nonlinear and linear fitting with the same experimental data.The results showed that the correlation coefficients of nonlinear fitting for Langmuir model,Freundlish model and pseudo-first-order kinetics model were greater than corresponding linear fitting and the parameters obtained by linear fitting were very different with the nonlinear fitting.But,the situation of fitting results for pseudo-second-order adsorption kinetics model and Van't Hoff model was different.The correlation coefficient of linear fitting was greater than or equal to nonlinear fitting correlation coefficient,and the relative errors of parameters obtained by nonlinear fitting and linear fitting were less than one percent.So it could be considered as a reference for adsorption models to determine whether linear fitting result is suitable.In summary,the nonlinear fitting is proposed to adsorption models processing.If adsorption models were fitted by linear fitting,it is likely to bring about a bigger error and affect the precision of the models.
In order to verify whether the fitting results were same by nonlinear fitting and linear fitting about various typical adsorption models,the paper took the experiment of sand adsorbing ammonia nitrogen.The Langmuir and Freundlish adsorption isotherm models,pseudo-first-order and pseudo-second-order adsorption kinetics models and Van't Hoff model of adsorption thermodynamics were fitted by nonlinear and linear fitting with the same experimental data.The results showed that the correlation coefficients of nonlinear fitting for Langmuir model,Freundlish model and pseudo-first-order kinetics model were greater than corresponding linear fitting and the parameters obtained by linear fitting were very different with the nonlinear fitting.But,the situation of fitting results for pseudo-second-order adsorption kinetics model and Van't Hoff model was different.The correlation coefficient of linear fitting was greater than or equal to nonlinear fitting correlation coefficient,and the relative errors of parameters obtained by nonlinear fitting and linear fitting were less than one percent.So it could be considered as a reference for adsorption models to determine whether linear fitting result is suitable.In summary,the nonlinear fitting is proposed to adsorption models processing.If adsorption models were fitted by linear fitting,it is likely to bring about a bigger error and affect the precision of the models.
引文
[1]谢宇.回归分析[M].2版.北京:社会科学文献出版社,2013.
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[3]孙同喜,郑萌璐,蒋轶锋,等.NaCl改性沸石对氨氮吸附性能的研究[J].环境污染与防治,2010,32(10): 46-50.
[4]张继义,韩雪,武英香,等.炭化小麦秸秆对水中氨氮吸附性能的研究[J].安全与环境学报,2012,12(1): 34-38.
[5]丁琨,徐镇男,张甲,等.酸性改性蜂巢石及其对废水中氨氮吸附能力的试验研究[J].长江大学学报(自然科学版),2016,13(1):25-29.
[6]王功芹,张硕,李大鹏,等.环境因子对海州湾表层沉积物中氨氮吸附-解吸的影响[J].生态环境学报,2017,26(1):95-103.
[7]张登宇,刘方,陈思琳,等.生物质炭对垃圾渗滤液中氨氮去除效果的研究[J].中国农学通报,2012,28 (14):264-268.
[8]李朝奎,黄力民,黄建柏.基于非线性误差模型的参数估计[J].测绘工程,2000,9(3):19-22.
[9]卢静波,吴艺能.非线性回归模型的线性变换和正交多项式回归[J].统计与决策,2009(23):13-14.
[10]李小荣,卜令兵,张剑锋.Langmuir方程对静态吸附数据拟合的研究[J].低温与特气,2011,29(3):13-16.
[11]占永革,黄湘燕,龚剑.化学分析中非线性曲线拟合结果的不确定度评定[J].冶金分析,2011,31(8): 26-30.
[12]魏世丽,葛永慧.一元非线性回归两种不同模型的比较[J].统计与决策,2015(4):29-31.
[13]李政兴.用线性回归方法拟合非线性模型的加权法[J].统计与决策,2000(9):12-13.
[2]张华,张学洪,白少元,等.柚皮活性炭对氨氮吸附性能研究[J].工业水处理,2012,32(6):56-59.
[3]孙同喜,郑萌璐,蒋轶锋,等.NaCl改性沸石对氨氮吸附性能的研究[J].环境污染与防治,2010,32(10): 46-50.
[4]张继义,韩雪,武英香,等.炭化小麦秸秆对水中氨氮吸附性能的研究[J].安全与环境学报,2012,12(1): 34-38.
[5]丁琨,徐镇男,张甲,等.酸性改性蜂巢石及其对废水中氨氮吸附能力的试验研究[J].长江大学学报(自然科学版),2016,13(1):25-29.
[6]王功芹,张硕,李大鹏,等.环境因子对海州湾表层沉积物中氨氮吸附-解吸的影响[J].生态环境学报,2017,26(1):95-103.
[7]张登宇,刘方,陈思琳,等.生物质炭对垃圾渗滤液中氨氮去除效果的研究[J].中国农学通报,2012,28 (14):264-268.
[8]李朝奎,黄力民,黄建柏.基于非线性误差模型的参数估计[J].测绘工程,2000,9(3):19-22.
[9]卢静波,吴艺能.非线性回归模型的线性变换和正交多项式回归[J].统计与决策,2009(23):13-14.
[10]李小荣,卜令兵,张剑锋.Langmuir方程对静态吸附数据拟合的研究[J].低温与特气,2011,29(3):13-16.
[11]占永革,黄湘燕,龚剑.化学分析中非线性曲线拟合结果的不确定度评定[J].冶金分析,2011,31(8): 26-30.
[12]魏世丽,葛永慧.一元非线性回归两种不同模型的比较[J].统计与决策,2015(4):29-31.
[13]李政兴.用线性回归方法拟合非线性模型的加权法[J].统计与决策,2000(9):12-13.
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