基于一级动力学模型的水培蔬菜滤床氮磷去除模拟

殷志平　 吴义锋　 吕锡武

(东南大学能源与环境学院, 南京 210096)



基于一级动力学模型的水培蔬菜滤床氮磷去除模拟

殷志平 吴义锋 吕锡武

(东南大学能源与环境学院, 南京 210096)

采用水培蔬菜滤床(HVFB)净化及经生化处理后的生活污水尾水,并选用一级动力学模型开展HVFB氮磷去除动力学试验研究．基于Arrhenius公式采用试验数据分析水温与一级反应面积速率常数K间关系,采用乘幂和指数回归方程拟合20 ℃时面积速率常数K20与水力负荷间关系,并构建滤床模型拓展式．Arrhenius拟合结果表明,番茄滤床的氨氮、总氮(TN)和总磷(TP)的温度系数θ值分别为1.08,1.06和1.01,空心菜滤床θ值分别为1.07,1.04和1.00,氨氮、TN的K值与水温呈显著正相关,氨氮的K值受水温影响更为敏感,TP的K值与水温无明显关系．在拟合K20与水力负荷关系上,乘幂回归整体上较指数回归具有更高的准确性．考虑了水温和水力负荷因素的一级动力学模型拓展式的预测具有较高的准确性和可靠性．增强TN去除效率(水温小于19.5 ℃)和TP去除效率(水温大于19.5 ℃),可有效提高HVFB整体进水水力负荷．

水培蔬菜滤床;氮;磷;一级动力学模型;一级动力学模型拓展式

水生植物滤床(aquatic plant filter bed, APFB)作为控制点源与非点源污染的一种新型生态技术[1-2],正受到人们的广泛关注．目前,APFB已用于城市暴雨径流[3]、河水[4]、冶炼厂废水[5]、水产养殖尾水[6]、农业废水[7]等的处理研究．APFB是由水生植物、水生动物及微生物构成的生态净化系统,净化机理包括根系过滤、沉淀、植物吸收、微生物作用等[8-9]．水培蔬菜滤床(hydroponic vegetable filter bed, HVFB)在具备APFB良好氮磷削减功能的同时,可产生一定的经济效益．

各国学者对APFB去除氮磷进行了相关研究[10-12],但对其预测方法与模型研究关注较少．与此同时,随着APFB关注度的提升和应用的普及，对其预测方法与模型研究提出了迫切需求．一级动力学模型作为应用最广泛的污染物去除预测模型[13],普遍用于湿地系统氮磷去除的模拟[14-16]．然而,Kadlec[17]指出由于参数的不确定性,一级动力学模型难以获得理想预测效果．一级动力学模型中速率常数常假定为定值,而研究表明其受环境和操作条件因素的影响[17-20]．Rousseau等[21]指出需特别关注模型中参数的不确定性．参数不确定性的研究对完善模型参数、提高HVFB模型的准确性和可靠性具有重要意义．

本文旨在建立简便、可靠的HVFB氮磷去除模型,以期用于HVFB的设计、性能预测与评价．选用一级动力学模型模拟HVFB氮磷去除效果,验证其适用性．研究水温、水力负荷与模型速率常数间的关系,并构建一级动力学模型拓展式．

1　试验材料及方法

1.1水培蔬菜滤床概况

水培蔬菜滤床系统(见图1)建于东南大学无锡分校,系统为砖砌混凝土结构,表面做防渗处理．滤床共有2组,每组长宽尺寸均为2 m×0.3 m,水深控制为10 cm,池底坡度为0.5%．2组滤床分别植入番茄和空心菜,番茄幼苗株高10 cm,栽种密度为35株/m2,以穿孔泡沫板固定番茄幼苗,空心菜栽种密度为30株/m2,试验期间植物长势随温度(季节)因素而变化,温度降低导致植物长势受到影响．

图1　滤床结构与原理示意图

蔬菜植入滤床40 d后开展试验,滤床系统进水为经水解池、好氧接触氧化池处理后的宿舍区生活污水．关于植物生长变化对去除效果的影响,在8月～12月间的温度变化较大程度反映了植物生长的变化,以温度作为生长变化的量化指标,将植物生长变化的影响并入温度因素中考虑．

1.2水样采集及分析

2014年8月～12月期间,取样时间间隔为3～4 d,水样于4 ℃保存待分析．检测指标为氨氮、硝态氮、总氮(TN)、总磷(TP)、DO、pH和温度(见表1)．检测项目氨氮、硝态氮、TN和TP均采用国标方法[22]分析．

1.3一级动力学模型

一级动力学模型K-C模型为

Cout=Cine-K/q

(1)

面积速率常数为

(2)

式中,Cout为出水浓度;Cin为进水浓度;K为一级反应面积速率常数;q为水力负荷．K值求解满足误差平方和最小，其中误差为出水实测值与出水预测值之差．

Arrhenius方程[23]表示温度对反应速率的影响,公式为

KT=K20θ(T-20)

(3)

式(3)的等价线性方程为

lnKT=lnK20+(T-20)lnθ

(4)

式中,KT为温度T时的面积速率常数;K20为20 ℃时的面积速率常数;θ为无量纲温度系数．采用式(4)的斜率与截距来计算式(3)中的参数．

采用相对均方根误差(RRMSE)来评价模拟准确性,数值范围为0～∞．数值越接近0,表明预测值与实测值越接近,即

(5)

2　结果与分析

2.1一级动力学模型适用性

表2中,8月～12月间,番茄滤床一级动力学模型氨氮、TN、TP的RRMSE分别为0.013～0.041,0.012～0.059和0.027～0.096；空心菜滤床氨氮、TN、TP的RRMSE分别为0.018～0.051,0.011～0.037和0.012～0.054.上述RRMSE值

均接近零．因此,一级动力学模型作为本试验滤床的预测模型是适宜的．Wang等[24]利用一级动力学模型进行浮床系统营养盐去除的研究,获得了理想效果．

2.2K随水温变化特征

图2为水温T与KT之间的相关关系.图2(a)～(d)表明,滤床氨氮、TN的KT值随水温的上升而增大．氮去除效率与水温呈正相关性,其原因是湿地系统脱氮效率易受温度影响[25-27]．图2(e)～(f)表明,TP的KT值随水温无明显变化趋势．

表2　K值和RRMSE

(d) 空心菜滤床,TN　(e) 番茄滤床,TP　(f) 空心菜滤床,TP

由表3可得,空心菜滤床的氨氮、TN和TP的K20均高于番茄滤床,空心菜滤床拥有更佳的氮磷去除功能．氨氮、TN和TP的K20对比表明,滤床对氨氮和TP的去除效率优于对TN的去除率.TN去除效率不佳原因为:① 进水碳氮比较低(m(C)/m(N)=2);② 滤床内为单一好氧环境．

表3中Arrhenius公式[23]拟合结果显示,氨氮、TN面积速率常数受水温影响明显．滤床的氨氮温度系数θ值均较TN的θ值大,即氨氮去除受温度影响更为敏感．Kadlec等[28-29]指出湿地系统

表3　Arrhenius拟合结果

TN的θ值为1.05.Nakasone等[30]指出湿地反硝化θ值为1.048．滤床内TP去除不受水温影响,根系截流和植物吸收是滤床除磷的主要途径[31]．番茄滤床TP的θ值为1.01,原因是低温下番茄生长活性降低,磷吸收效果有所下降．Kadlec等[28-29]指出湿地系统去除TP的θ值为1.0．

2.3水力负荷对K20的影响

图3为水力负荷与K20(由式(3)计算)间的相关关系.由图可见,氨氮、TN、TP的K20均随水力负荷的提高而增大,这与Kadlec[17]和Rousseau等[21]的研究结果一致．通过乘幂[17]和指数[18]回归方程拟合K20与水力负荷间关系，即

K20=K′qm

(6)

K20=K″enq

(7)

式中,K′，K″，m和n为无量纲负荷系数，见表4．

(d) 空心菜滤床，TN　(e) 番茄滤床，TP　(f) 空心菜滤床，TP

参数番茄滤床空心菜滤床氨氮TNTP氨氮TNTP乘幂K'0.1070.0760.0850.1670.1180.147m0.2220.2570.1580.2890.3390.199R20.6470.5380.3750.7100.7690.381指数K″0.0620.0390.0560.0810.0500.088n0.8551.0110.6801.1151.3320.818R20.6110.5340.4430.6760.7560.410

由表4可见，空心菜滤床的m和n值高于番茄滤床,表明同等水力负荷增量下,空心菜滤床K20增速较快,即其具有较高的负荷缓冲能力．

由表4中R值表明,乘幂回归比指数回归整体具有更高的拟合度．

2.4一级动力学模型拓展式

2.4.1模型拓展式评价

在滤床一级动力学模型中考虑水温和水力负荷因素,结合式(1)、(3)和(6),则可构建如下方程：

Cout=Cinexp(-K′qmθT-20/q)=

Cinexp(-K′qm-1θT-20)

(8)

空心菜滤床模型拓展式为

Cout,NH3-N=Cin,NH3-Nexp(-0.167q-0.7111.07T-20)

Cout,TN=Cin,TNexp(-0.118q-0.6611.04T-20)

Cout,TP=Cin,TPexp(-0.147q-0.8011.00T-20)

式中，Cout,NH3-N,Cout,TN,Cout,TP分别为氨氮、TN和TP出水浓度；Cin,NH3-N,Cin,TN,Cin,TP分别为氨氮、TN和TP进水浓度.

利用线性回归方程y=αx评价出水实测值与预测值间偏差．最佳情况为所有数据点全部位于斜线y=x上(见图4),即α值越接近1,实测值与预测值之间偏差越小,模型准确性越高．图4(a)～(c)中氨氮、TN和TP的α值分别为1.033，0.975和0.965,均接近1．其中,出水氨氮预测值略高于实测值,TN，TP的预测值略低于实测值．α值和R2(0.476,0.623,0.877)表明,式(8)对试验滤床氮磷去除的预测具备准确性．

2.4.2模型拓展式应用

图5为本试验进水水质和滤床结构条件下,出水氮磷指标分别达到《城镇污水处理厂污染物排放标准》(GB18918—2002)一级A排放标准的最大允许水力负荷线,3条负荷线下方为达标区．为确保氮磷出水均达到一级A排放标准,水力负荷应取氨氮、TN和TP中的最小值．图5表明,当水温低于19.5 ℃时,TN为水力负荷最小值,水温高于19.5 ℃时,TP为水力负荷最小值．为有效增加滤床整体进水水力负荷,应在水温低于19.5 ℃时提高TN去除效率,在水温高于19.5 ℃时提高TP去除效率．

(a) 空心菜滤床,氨氮

(b) 空心菜滤床,TN

(c) 空心菜滤床,TP

图5　达标水力负荷线

3　结论

1) 与番茄滤床相比,空心菜滤床的氮磷去除能力更优,且具备较高的负荷缓冲能力．HVFB去除氮磷效率大小顺序为氨氮、TP、TN．

2) HVFB氨氮、TN的K值与水温呈正相关性.Arrhenius拟合结果表明,番茄滤床氨氮和TN的θ值分别为1.08和1.06,空心菜滤床氨氮和TN的θ值分别为1.07和1.04,氨氮去除率受水温影响更为敏感．TP的K值基本不受水温影响．

3) 氨氮、TN和TP的K20随水力负荷的提高而增大．氨氮和TN的乘幂回归R2值较指数回归R2值更接近于1,而TP结果则相反．乘幂回归方程整体具有更高拟合度．

4) 氨氮、TN和TP的α值(1.033，0.975和0.965)和R2(0.476,0.623,0.877)结果表明,考虑了水温和水力负荷因素的模型拓展式对滤床氮磷去除的预测具有准确性和可靠性．

5) 提升TN去除效率(水温小于19.5 ℃)和TP去除效率(水温大于19.5 ℃),有利于提高滤床整体进水水力负荷．

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Simulation of nitrogen and phosphorus removal in hydroponic vegetable filter bed based on first-order kinetics model

Yin Zhiping Wu Yifeng Lü Xiwu

(School of Energy and Environment, Southeast University, Nanjing 210096, China)

The kinetics studies on nitrogen and phosphorus removal in hydroponic vegetable filter beds (HVFB) were conducted by using first-order kinetics model. The raw water was domestic sewage which were treated by biochemical treatment processes. The dependence of first-order area rate constantKof the water temperature was estimated by the Arrhenius equation, and the relationship betweenK20and hydraulic loading rateqwas analyzed by power and exponential regression equations. Meanwhile, the extended kinetics model of the filter bed was constructed. The results show that, for the tomato filter bed, the temperature coefficientθvalues of ammonia nitrogen, total nitrogen (TN), and total phosphorus (TP) were 1.08, 1.06, and 1.01, respectively, and theθvalues in water spinach filter bed were 1.07, 1.04, and 1.00, respectively. TheKvalues of ammonia nitrogen and TN have significant positive correlation with the water temperature, and theKvalues of ammonia nitrogen are more sensitive to water temperature change, but there are no significant differences between theKvalues at different water temperatures for TP. Compared with exponential regression equation, power regression equation is more suitable for describing the relationship betweenK20andq. The extended first-order models, considering the influences of the water temperature andqonK, have a certain accuracy and higher reliability in predicting removal results of filter beds. Enhanced TN removal efficiency (water temperature is lower than 19.5 ℃) and TP removal efficiency (water temperature is higher than 19.5 ℃) will cause an overall increase on hydraulic loading rate of HVFB.

hydroponic vegetable filter bed; nitrogen; phosphorus; first-order kinetics model; extended first-order kinetics model

10.3969/j.issn.1001-0505.2016.04.023

2015-11-04.作者简介: 殷志平(1991—),男,硕士生;吴义锋(联系人),男,博士,副教授,shinfun@seu.edu.cn.

“十二五”国家科技支撑计划资助项目(2013BAJ10B13).

10.3969/j.issn.1001-0505.2016.04.023.

X171

A

1001-0505(2016)04-0812-06

引用本文: 殷志平,吴义锋,吕锡武.基于一级动力学模型的水培蔬菜滤床氮磷去除模拟[J].东南大学学报(自然科学版),2016,46(4):812-817.