殷志平　 吳義鋒　 呂錫武

(東南大學(xué)能源與環(huán)境學(xué)院, 南京 210096)

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基于一級(jí)動(dòng)力學(xué)模型的水培蔬菜濾床氮磷去除模擬

殷志平 吳義鋒 呂錫武

(東南大學(xué)能源與環(huán)境學(xué)院, 南京 210096)

采用水培蔬菜濾床(HVFB)凈化及經(jīng)生化處理后的生活污水尾水,并選用一級(jí)動(dòng)力學(xué)模型開(kāi)展HVFB氮磷去除動(dòng)力學(xué)試驗(yàn)研究．基于Arrhenius公式采用試驗(yàn)數(shù)據(jù)分析水溫與一級(jí)反應(yīng)面積速率常數(shù)K間關(guān)系,采用乘冪和指數(shù)回歸方程擬合20 ℃時(shí)面積速率常數(shù)K20與水力負(fù)荷間關(guān)系,并構(gòu)建濾床模型拓展式．Arrhenius擬合結(jié)果表明,番茄濾床的氨氮、總氮(TN)和總磷(TP)的溫度系數(shù)θ值分別為1.08,1.06和1.01,空心菜濾床θ值分別為1.07,1.04和1.00,氨氮、TN的K值與水溫呈顯著正相關(guān),氨氮的K值受水溫影響更為敏感,TP的K值與水溫?zé)o明顯關(guān)系．在擬合K20與水力負(fù)荷關(guān)系上,乘冪回歸整體上較指數(shù)回歸具有更高的準(zhǔn)確性．考慮了水溫和水力負(fù)荷因素的一級(jí)動(dòng)力學(xué)模型拓展式的預(yù)測(cè)具有較高的準(zhǔn)確性和可靠性．增強(qiáng)TN去除效率(水溫小于19.5 ℃)和TP去除效率(水溫大于19.5 ℃),可有效提高HVFB整體進(jìn)水水力負(fù)荷．

水培蔬菜濾床;氮;磷;一級(jí)動(dòng)力學(xué)模型;一級(jí)動(dòng)力學(xué)模型拓展式

水生植物濾床(aquatic plant filter bed, APFB)作為控制點(diǎn)源與非點(diǎn)源污染的一種新型生態(tài)技術(shù)[1-2],正受到人們的廣泛關(guān)注．目前,APFB已用于城市暴雨徑流[3]、河水[4]、冶煉廠廢水[5]、水產(chǎn)養(yǎng)殖尾水[6]、農(nóng)業(yè)廢水[7]等的處理研究．APFB是由水生植物、水生動(dòng)物及微生物構(gòu)成的生態(tài)凈化系統(tǒng),凈化機(jī)理包括根系過(guò)濾、沉淀、植物吸收、微生物作用等[8-9]．水培蔬菜濾床(hydroponic vegetable filter bed, HVFB)在具備APFB良好氮磷削減功能的同時(shí),可產(chǎn)生一定的經(jīng)濟(jì)效益．

各國(guó)學(xué)者對(duì)APFB去除氮磷進(jìn)行了相關(guān)研究[10-12],但對(duì)其預(yù)測(cè)方法與模型研究關(guān)注較少．與此同時(shí),隨著APFB關(guān)注度的提升和應(yīng)用的普及，對(duì)其預(yù)測(cè)方法與模型研究提出了迫切需求．一級(jí)動(dòng)力學(xué)模型作為應(yīng)用最廣泛的污染物去除預(yù)測(cè)模型[13],普遍用于濕地系統(tǒng)氮磷去除的模擬[14-16]．然而,Kadlec[17]指出由于參數(shù)的不確定性,一級(jí)動(dòng)力學(xué)模型難以獲得理想預(yù)測(cè)效果．一級(jí)動(dòng)力學(xué)模型中速率常數(shù)常假定為定值,而研究表明其受環(huán)境和操作條件因素的影響[17-20]．Rousseau等[21]指出需特別關(guān)注模型中參數(shù)的不確定性．參數(shù)不確定性的研究對(duì)完善模型參數(shù)、提高HVFB模型的準(zhǔn)確性和可靠性具有重要意義．

本文旨在建立簡(jiǎn)便、可靠的HVFB氮磷去除模型,以期用于HVFB的設(shè)計(jì)、性能預(yù)測(cè)與評(píng)價(jià)．選用一級(jí)動(dòng)力學(xué)模型模擬HVFB氮磷去除效果,驗(yàn)證其適用性．研究水溫、水力負(fù)荷與模型速率常數(shù)間的關(guān)系,并構(gòu)建一級(jí)動(dòng)力學(xué)模型拓展式．

1　試驗(yàn)材料及方法

1.1水培蔬菜濾床概況

水培蔬菜濾床系統(tǒng)(見(jiàn)圖1)建于東南大學(xué)無(wú)錫分校,系統(tǒng)為磚砌混凝土結(jié)構(gòu),表面做防滲處理．濾床共有2組,每組長(zhǎng)寬尺寸均為2 m×0.3 m,水深控制為10 cm,池底坡度為0.5%．2組濾床分別植入番茄和空心菜,番茄幼苗株高10 cm,栽種密度為35株/m2,以穿孔泡沫板固定番茄幼苗,空心菜栽種密度為30株/m2,試驗(yàn)期間植物長(zhǎng)勢(shì)隨溫度(季節(jié))因素而變化,溫度降低導(dǎo)致植物長(zhǎng)勢(shì)受到影響．

圖1　濾床結(jié)構(gòu)與原理示意圖

蔬菜植入濾床40 d后開(kāi)展試驗(yàn),濾床系統(tǒng)進(jìn)水為經(jīng)水解池、好氧接觸氧化池處理后的宿舍區(qū)生活污水．關(guān)于植物生長(zhǎng)變化對(duì)去除效果的影響,在8月～12月間的溫度變化較大程度反映了植物生長(zhǎng)的變化,以溫度作為生長(zhǎng)變化的量化指標(biāo),將植物生長(zhǎng)變化的影響并入溫度因素中考慮．

1.2水樣采集及分析

2014年8月～12月期間,取樣時(shí)間間隔為3～4 d,水樣于4 ℃保存待分析．檢測(cè)指標(biāo)為氨氮、硝態(tài)氮、總氮(TN)、總磷(TP)、DO、pH和溫度(見(jiàn)表1)．檢測(cè)項(xiàng)目氨氮、硝態(tài)氮、TN和TP均采用國(guó)標(biāo)方法[22]分析．

1.3一級(jí)動(dòng)力學(xué)模型

一級(jí)動(dòng)力學(xué)模型K-C模型為

Cout=Cine-K/q

(1)

面積速率常數(shù)為

(2)

式中,Cout為出水濃度;Cin為進(jìn)水濃度;K為一級(jí)反應(yīng)面積速率常數(shù);q為水力負(fù)荷．K值求解滿足誤差平方和最小，其中誤差為出水實(shí)測(cè)值與出水預(yù)測(cè)值之差．

Arrhenius方程[23]表示溫度對(duì)反應(yīng)速率的影響,公式為

KT=K20θ(T-20)

(3)

式(3)的等價(jià)線性方程為

lnKT=lnK20+(T-20)lnθ

(4)

式中,KT為溫度T時(shí)的面積速率常數(shù);K20為20 ℃時(shí)的面積速率常數(shù);θ為無(wú)量綱溫度系數(shù)．采用式(4)的斜率與截距來(lái)計(jì)算式(3)中的參數(shù)．

采用相對(duì)均方根誤差(RRMSE)來(lái)評(píng)價(jià)模擬準(zhǔn)確性,數(shù)值范圍為0～∞．?dāng)?shù)值越接近0,表明預(yù)測(cè)值與實(shí)測(cè)值越接近,即

(5)

2　結(jié)果與分析

2.1一級(jí)動(dòng)力學(xué)模型適用性

表2中,8月～12月間,番茄濾床一級(jí)動(dòng)力學(xué)模型氨氮、TN、TP的RRMSE分別為0.013～0.041,0.012～0.059和0.027～0.096；空心菜濾床氨氮、TN、TP的RRMSE分別為0.018～0.051,0.011～0.037和0.012～0.054.上述RRMSE值

均接近零．因此,一級(jí)動(dòng)力學(xué)模型作為本試驗(yàn)濾床的預(yù)測(cè)模型是適宜的．Wang等[24]利用一級(jí)動(dòng)力學(xué)模型進(jìn)行浮床系統(tǒng)營(yíng)養(yǎng)鹽去除的研究,獲得了理想效果．

2.2K隨水溫變化特征

圖2為水溫T與KT之間的相關(guān)關(guān)系.圖2(a)～(d)表明,濾床氨氮、TN的KT值隨水溫的上升而增大．氮去除效率與水溫呈正相關(guān)性,其原因是濕地系統(tǒng)脫氮效率易受溫度影響[25-27]．圖2(e)～(f)表明,TP的KT值隨水溫?zé)o明顯變化趨勢(shì)．

表2　K值和RRMSE

(d) 空心菜濾床,TN　(e) 番茄濾床,TP　(f) 空心菜濾床,TP

由表3可得,空心菜濾床的氨氮、TN和TP的K20均高于番茄濾床,空心菜濾床擁有更佳的氮磷去除功能．氨氮、TN和TP的K20對(duì)比表明,濾床對(duì)氨氮和TP的去除效率優(yōu)于對(duì)TN的去除率.TN去除效率不佳原因?yàn)?① 進(jìn)水碳氮比較低(m(C)/m(N)=2);② 濾床內(nèi)為單一好氧環(huán)境．

表3中Arrhenius公式[23]擬合結(jié)果顯示,氨氮、TN面積速率常數(shù)受水溫影響明顯．濾床的氨氮溫度系數(shù)θ值均較TN的θ值大,即氨氮去除受溫度影響更為敏感．Kadlec等[28-29]指出濕地系統(tǒng)

表3　Arrhenius擬合結(jié)果

TN的θ值為1.05.Nakasone等[30]指出濕地反硝化θ值為1.048．濾床內(nèi)TP去除不受水溫影響,根系截流和植物吸收是濾床除磷的主要途徑[31]．番茄濾床TP的θ值為1.01,原因是低溫下番茄生長(zhǎng)活性降低,磷吸收效果有所下降．Kadlec等[28-29]指出濕地系統(tǒng)去除TP的θ值為1.0．

2.3水力負(fù)荷對(duì)K20的影響

圖3為水力負(fù)荷與K20(由式(3)計(jì)算)間的相關(guān)關(guān)系.由圖可見(jiàn),氨氮、TN、TP的K20均隨水力負(fù)荷的提高而增大,這與Kadlec[17]和Rousseau等[21]的研究結(jié)果一致．通過(guò)乘冪[17]和指數(shù)[18]回歸方程擬合K20與水力負(fù)荷間關(guān)系，即

K20=K′qm

(6)

K20=K″e(cuò)nq

(7)

式中,K′，K″，m和n為無(wú)量綱負(fù)荷系數(shù)，見(jiàn)表4．

(d) 空心菜濾床，TN　(e) 番茄濾床，TP　(f) 空心菜濾床，TP

參數(shù)番茄濾床空心菜濾床氨氮TNTP氨氮TNTP乘冪K'0.1070.0760.0850.1670.1180.147m0.2220.2570.1580.2890.3390.199R20.6470.5380.3750.7100.7690.381指數(shù)K″0.0620.0390.0560.0810.0500.088n0.8551.0110.6801.1151.3320.818R20.6110.5340.4430.6760.7560.410

由表4可見(jiàn)，空心菜濾床的m和n值高于番茄濾床,表明同等水力負(fù)荷增量下,空心菜濾床K20增速較快,即其具有較高的負(fù)荷緩沖能力．

由表4中R值表明,乘冪回歸比指數(shù)回歸整體具有更高的擬合度．

2.4一級(jí)動(dòng)力學(xué)模型拓展式

2.4.1模型拓展式評(píng)價(jià)

在濾床一級(jí)動(dòng)力學(xué)模型中考慮水溫和水力負(fù)荷因素,結(jié)合式(1)、(3)和(6),則可構(gòu)建如下方程：

Cout=Cinexp(-K′qmθT-20/q)=

Cinexp(-K′qm-1θT-20)

(8)

空心菜濾床模型拓展式為

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分別為氨氮、TN和TP出水濃度；Cin,NH3-N,Cin,TN,Cin,TP分別為氨氮、TN和TP進(jìn)水濃度.

利用線性回歸方程y=αx評(píng)價(jià)出水實(shí)測(cè)值與預(yù)測(cè)值間偏差．最佳情況為所有數(shù)據(jù)點(diǎn)全部位于斜線y=x上(見(jiàn)圖4),即α值越接近1,實(shí)測(cè)值與預(yù)測(cè)值之間偏差越小,模型準(zhǔn)確性越高．圖4(a)～(c)中氨氮、TN和TP的α值分別為1.033，0.975和0.965,均接近1．其中,出水氨氮預(yù)測(cè)值略高于實(shí)測(cè)值,TN，TP的預(yù)測(cè)值略低于實(shí)測(cè)值．α值和R2(0.476,0.623,0.877)表明,式(8)對(duì)試驗(yàn)濾床氮磷去除的預(yù)測(cè)具備準(zhǔn)確性．

2.4.2模型拓展式應(yīng)用

圖5為本試驗(yàn)進(jìn)水水質(zhì)和濾床結(jié)構(gòu)條件下,出水氮磷指標(biāo)分別達(dá)到《城鎮(zhèn)污水處理廠污染物排放標(biāo)準(zhǔn)》(GB18918—2002)一級(jí)A排放標(biāo)準(zhǔn)的最大允許水力負(fù)荷線,3條負(fù)荷線下方為達(dá)標(biāo)區(qū)．為確保氮磷出水均達(dá)到一級(jí)A排放標(biāo)準(zhǔn),水力負(fù)荷應(yīng)取氨氮、TN和TP中的最小值．圖5表明,當(dāng)水溫低于19.5 ℃時(shí),TN為水力負(fù)荷最小值,水溫高于19.5 ℃時(shí),TP為水力負(fù)荷最小值．為有效增加濾床整體進(jìn)水水力負(fù)荷,應(yīng)在水溫低于19.5 ℃時(shí)提高TN去除效率,在水溫高于19.5 ℃時(shí)提高TP去除效率．

(a) 空心菜濾床,氨氮

(b) 空心菜濾床,TN

(c) 空心菜濾床,TP

圖5　達(dá)標(biāo)水力負(fù)荷線

3　結(jié)論

1) 與番茄濾床相比,空心菜濾床的氮磷去除能力更優(yōu),且具備較高的負(fù)荷緩沖能力．HVFB去除氮磷效率大小順序?yàn)榘钡?、TP、TN．

2) HVFB氨氮、TN的K值與水溫呈正相關(guān)性.Arrhenius擬合結(jié)果表明,番茄濾床氨氮和TN的θ值分別為1.08和1.06,空心菜濾床氨氮和TN的θ值分別為1.07和1.04,氨氮去除率受水溫影響更為敏感．TP的K值基本不受水溫影響．

3) 氨氮、TN和TP的K20隨水力負(fù)荷的提高而增大．氨氮和TN的乘冪回歸R2值較指數(shù)回歸R2值更接近于1,而TP結(jié)果則相反．乘冪回歸方程整體具有更高擬合度．

4) 氨氮、TN和TP的α值(1.033，0.975和0.965)和R2(0.476,0.623,0.877)結(jié)果表明,考慮了水溫和水力負(fù)荷因素的模型拓展式對(duì)濾床氮磷去除的預(yù)測(cè)具有準(zhǔn)確性和可靠性．

5) 提升TN去除效率(水溫小于19.5 ℃)和TP去除效率(水溫大于19.5 ℃),有利于提高濾床整體進(jìn)水水力負(fù)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.作者簡(jiǎn)介: 殷志平(1991—),男,碩士生;吳義鋒(聯(lián)系人),男,博士,副教授,shinfun@seu.edu.cn.

“十二五”國(guó)家科技支撐計(jì)劃資助項(xiàng)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,吳義鋒,呂錫武.基于一級(jí)動(dòng)力學(xué)模型的水培蔬菜濾床氮磷去除模擬[J].東南大學(xué)學(xué)報(bào)(自然科學(xué)版),2016,46(4):812-817.