孫東霞,周子安,馮志合,胡修玉,祁光霞,董黎明*

pH值調控檸檬酸污泥厭氧發(fā)酵產酸及碳源潛力研究

孫東霞1,周子安1,馮志合2,胡修玉2,祁光霞1,董黎明1*

(1.北京工商大學,中國輕工業(yè)清潔生產和資源綜合利用重點實驗室,國家環(huán)境保護食品鏈污染防治重點實驗室,北京 100048；2.中國生物發(fā)酵產業(yè)協(xié)會,北京 100083)

以檸檬酸廢水厭氧顆粒污泥為接種物,在不同pH值調控條件下開展檸檬酸生產廢水剩余活性污泥厭氧發(fā)酵產酸研究.通過對發(fā)酵液揮發(fā)性脂肪酸(VFAs)、有機質、氮磷和污泥脫水性能的分析,探討了檸檬酸污泥厭氧產酸機制.結果表明,pH310的堿性條件更有利于有機質的溶出從而促進VFAs的產生.三維熒光光譜分析發(fā)現在恒定pH值下腐殖酸(HA)和富里酸(FA)會大量溶出降低VFAs的產量.初始pH=10是檸檬酸污泥厭氧產酸的最佳pH值,發(fā)酵4d的VFAs濃度最高達(6681.47±126.82) mg COD/L,是文獻報道中市政污泥產酸量的近2倍,其中乙酸占比49.8%,發(fā)酵后產酸功能菌Chloroflexi、Bacteroidota的相對豐度分別由初始的9.52%、10.87%增至16.84%、14.39%,污泥歸一化毛細吸水時間(CST)為(11.34±0.27) s×L/g,脫水性能良好,發(fā)酵液TP濃度為(20.45±0.33) mg/L.研究表明,利用檸檬酸剩余活性污泥堿性厭氧發(fā)酵產酸作為污水處理過程中的外加碳源具有較大潛力.

pH值調控；檸檬酸污泥；堿性厭氧發(fā)酵；揮發(fā)性脂肪酸；污泥脫水性能

城市污水處理廠通常采用生物處理技術去除廢水中的營養(yǎng)物質以緩解水體富營養(yǎng)化,然而目前國內污水進水碳源不足極大地限制了氮、磷的去除效率,因此在廢水處理過程中通常使用甲醇、乙醇和乙酸作為有機碳源,但化學藥品的添加不僅增加了運營成本也會造成二次污染[1-2].污水好氧處理的剩余活性污泥富含豐富的有機物,通過厭氧發(fā)酵可產生揮發(fā)性脂肪酸(VFAs),將其作為污水處理的有機碳源,可實現對剩余活性污泥的資源化利用[3].

影響污泥厭氧發(fā)酵的因素包括溫度、pH值、微生物、水力停留時間等[4],其中pH值不僅影響污泥水解和產物組成,還影響微生物群落變化,是污泥厭氧發(fā)酵產生VFAs的最重要因素之一[5].然而產酸發(fā)酵細菌對pH值的適應性較強[6-7],有研究表明酸性啟動(pH=6.0)VFAs最高累積質量濃度為1683.5mg/L,比堿性啟動模式(pH=10.0)提高了37.5%[8].但堿性條件有利于促進有機物水解,提供高濃度的可溶性底物(SCOD),增加VFAs的產生[5].而通過不斷調控pH值,堿性發(fā)酵(pH=10.0)VFAs產量為2901.33mg COD/L,是酸性發(fā)酵的2.7倍[9].由于污泥種類以及實驗條件的不同,產酸條件所需的最優(yōu)pH值不同,但高濃度的SCOD更有利于VFAs的產生結論一致[4].有研究者[10-12]已建立完整的污水污泥堿性厭氧發(fā)酵產VFAs和作為外部碳源提高污水廠的生物脫氮除磷的工藝系統(tǒng),長期運行結果表明,該系統(tǒng)可實現污泥減量和碳源回收,減少約54%的污泥量,平均VFAs產量達到261.32mg COD/g VSS,該系統(tǒng)凈利潤為9.12美元/m3,比污泥厭氧消化產沼氣(3.71美元/m3)有更大的經濟優(yōu)勢.但目前基本是針對市政污泥產酸條件與機制的研究,鮮見對工業(yè)污泥的發(fā)酵產酸研究.而我國是檸檬酸生產大國,占世界檸檬酸產量的70%以上,產量每年增長7%,其主要利用玉米進行發(fā)酵生產,產生的廢水可生化性高,經厭氧處理產生的顆粒污泥是重要的微生物源,再經好氧處理會產生大量有機質含量較高的剩余活性污泥[13],其處理處置成本約占污水處理廠運營成本的60%[14].相比市政污泥,其有機質含量較高,可為發(fā)酵提供充足的底物,因此本研究通過分析不同pH值對檸檬酸剩余活性污泥厭氧發(fā)酵產VFAs的影響,探討發(fā)酵過程VFAs積累的機制與發(fā)酵液作污水處理過程中外源碳源的潛力,為發(fā)酵工業(yè)剩余活性污泥的資源化利用提供參考.

1 材料與方法

1.1 實驗材料

選取山東省某檸檬酸生產企業(yè)好氧生化處理的剩余污泥和厭氧顆粒污泥,其中厭氧顆粒污泥作為剩余污泥厭氧發(fā)酵的初始菌種,經自然沉降棄去上清液,保存在4℃冰箱中備用.實驗時剩余污泥過60目網篩去除沙礫,其含固率(TS)為(4.24±0.64)%,有機物含量(VS)為(50.10±1.21)%,溶解性化學總需氧量(SCOD)為(687.50±51.03) mg/L,可溶性蛋白質(PN)為(253.33±11.11) mg/L,可溶性多糖(PS)為(19.13±2.37) mg/L,總磷(TP)為(23.17±1.31) mg/L,氨氮(NH3-N)為(294.91±12.02) mg/L.

1.2 實驗方法

采用序批式實驗,將剩余污泥和厭氧顆粒污泥按照質量比TS=4:1的比例混合均勻,測得pH= (7.12±0.22),以此為空白對照組(Control).將300g混合污泥加入500mL厭氧發(fā)酵瓶中,通入氮氣,保證厭氧密閉環(huán)境,在(36±2)℃,(120±10) r/min的水浴搖床中進行厭氧發(fā)酵.

使用6mol/L的HCl或NaOH,將發(fā)酵罐中混合污泥分別調節(jié)pH值為5、6、8、9、10、11、12,此后不再調控pH值,記為初始pH值調控組(pH),同時對產生VFAs的實驗組再次進行維持整個發(fā)酵過程恒定pH值的實驗,記為恒定pH值調控組(C-pH).

所有發(fā)酵罐均設置平行實驗,在VFAs連續(xù)下降3d后停止實驗.取調節(jié)pH值后的混合污泥樣品記為0d,間隔24h取樣,樣品經9000r/min離心10min,上清液過0.45μm濾膜后用于指標測定,沉淀測定微生物.

1.3 指標測定

參照《城市污水處理廠污泥檢測方法》(CTJ221-2005)測定樣品的TS和VS,TP和NH3-N分別采用鉬酸銨分光光度法和納氏試劑分光光度法測定[15],用Lowry-Folin法和蒽酮-硫酸法分別測定PN和PS[16],毛細吸水時間(CST)使用CST測定儀(TR04-304M, Triton,英國)測定,結果歸一化[9],見式(1).

式中:CST為歸一化結果,s·L/g; CST為儀器測定的毛細吸水時間,s; TS為污泥含固率,g/L.

Zeta電位使用激光Zeta粒度分析儀(Zetasizer Nano ZS,馬爾文,英國)測定;溶解性總有機碳(DOC)使用DOC分析儀(VarioEL III, Elementar,德國)測定;使用哈克旋轉流變儀(HAAKE MARS III, Thermo Scientific,美國),選擇速率與黏度模型,CC25DIN Ti轉子,剪切率10～300s-1,在25℃下對污泥樣品流變特性進行測定[17];VFAs采用氣相色譜儀(GC-2014,島津,日本)檢測,換算關系為:1.07g COD/g乙酸, 1.51g COD/g丙酸,1.82g COD/g丁酸和2.04g COD/g戊酸[2].樣品經處理后(UV254<0.3),使用三維熒光光譜儀(Spectrofluorometer FS5,愛丁堡,英國)在x/m= 220～550nm/240～600nm,間隔5nm,設置中扣除空白散射,測其三維熒光(3D-EEM)譜圖,結果采用MATLAB 2018b進行平行因子(PARAFAC)分析[18-19].微生物由上海美吉生物公司測定,樣品經DNA提取后,使用引物(338F和806R)進行PCR擴增后,對16S rDNA的V3-V4可變區(qū)基因進行測序分析[1].所有數據使用origin 2018作圖.樣品進行了3次平行測定.

2 結果分析

2.1 初始pH值對污泥發(fā)酵性能的影響

SCOD是反映污泥水解和酸化程度的重要指標,如圖1(a)所示,在0d時酸堿的加入都促進污泥水解,但pH310的條件下SCOD濃度更高,污泥水解的效果更佳.根據厭氧發(fā)酵的主要產物甲烷和VFAs的變化情況(圖1(b)),初始pH=5～9的條件有利于甲烷的產生,其中Control組累計最大甲烷產量為(40.25±2.86)mL/g VS,其他條件下甲烷產量降低甚至完全消失,是產甲烷菌的活性受到抑制或喪失所致,甲烷的產生消耗有機物,與發(fā)酵后SCOD下降結果一致.初始pH=10～12的實驗組厭氧發(fā)酵后(8d)產生了大量VFAs,導致SCOD濃度增加,其中pH=10的實驗組在8d時VFAs含量最高為(3149.45±202.53) mg COD/L.因此初始pH=10～12有利于檸檬酸剩余污泥厭氧發(fā)酵VFAs的積累,這與Wu等[2]和Ma等[20]對不同pH值下污泥厭氧發(fā)酵得出堿性條件更利于污泥厭氧產VFAs的結論相一致.

圖1 不同初始pH值厭氧發(fā)酵前后SCOD濃度與發(fā)酵過程累積CH4產量和第8d的VFAs濃度變化

2.2 恒定和初始堿性條件對檸檬酸污泥厭氧產酸的影響

2.2.1 恒定和初始堿性條件對VFAs產量的影響 對產生VFAs的實驗組(pH=10、11、12)進行維持恒定pH值的厭氧發(fā)酵實驗,如圖2所示.不同條件總VFAs的最大濃度不同,其順序為:pH=10 ((6681.47± 126.82)mg COD/L)>pH=11((5964.85±524.72) mg COD/L)> C-pH=11((4902.85±596.79)mg COD/L) >C-pH=10 ((4427.41±111.48)mg COD/L)>C-pH=12 ((3321.91±461.07)mg COD/L)>pH=12((2746.54± 55.82) mg COD/ L),pH值為12的兩組VFAs濃度低,是因為大多數產酸菌不易在pH312條件下存活[3].此外到達總VFAs最大濃度的時間亦不同,pH=10時間最短僅為4d,其次是pH=11和C-pH=10為5d,時間延長VFAs出現下降趨勢,可能是底物不足或被產酸菌利用的結果[2].因此pH=10是檸檬酸剩余污泥厭氧產酸較佳的條件,約為相似條件下的市政污泥厭氧發(fā)酵產VFAs濃度的2倍(最大VFAs濃度為2500～ 3000mg COD/L,時間為5～6d)[9,21].不同條件對VFAs的組成有不同影響,其中乙酸占VFAs總量的45%～ 66%,決定VFAs變化總趨勢,因為大多數微生物都能產生乙酸[22],同時它是污水處理過程中受歡迎的碳源,含量越高碳源利用潛力越大[22].其次是異戊酸和丙酸占比為8%～25%,異丁酸、正丁酸和正戊酸由于分解較快[23]僅占2%～13%.

2.2.2 堿性厭氧產酸發(fā)酵過程中有機質的變化 如圖3所示,SCOD與DOC變化趨勢基本與PN、PS和VFAs濃度變化相一致.在0d時PN、PS的水解程度與堿性pH值呈正相關,但PN的水解濃度是Control組的2.66～4.90倍,高于PS(1.10～2.29倍),堿性條件更有利于PN的析出[2,20].隨著發(fā)酵時間的延長Control組PN濃度基本不變,而PS有明顯的先升后降趨勢,可能是中性條件下更有利于產甲烷菌對PS的水解和利用.相反在恒定pH值的厭氧發(fā)酵過程中PN、PS濃度逐漸升高,是堿性環(huán)境促進污泥絮體的破壞所致[3,24],在5～8d時PN快速下降,而此時VFAs濃度沒有明顯上升,可能是因為強堿與氨基、羧基反應生成鹽導致蛋白質變性.pH=11、12的實驗組發(fā)酵過程中PN和PS呈不明顯上升趨勢,在pH=10的實驗組PN和PS變化趨勢顯著,0～4d時VFAs濃度迅速上升,此時PN濃度下降而PS上升,可能是產酸菌對PN的利用率高于PN的水解率和PS的利用率,在4～5d時PN和PS可能達到此條件下最大水解程度,時間延長產酸底物不斷減少VFAs濃度下降.

圖2 不同堿性條件對VFAs產量及組成的影響

圖3 堿性厭氧產酸發(fā)酵過程中SCOD、DOC、PN和PS的變化

2.2.3 熒光組分的變化 通過PARAFAC分析對上清液3D-EEM光譜進行拆分發(fā)現,3種主要熒光物質[25](圖4),分別為色氨酸類蛋白質(TPN):x/m= 275nm/360nm,腐殖酸類物質(HA):x/m=360(415) nm/470nm和富里酸類物質(FA):x/m=320nm/ 400nm,同時得到最大熒光max圖5,通常TPN、FA和HA都被認為是難生物降解的化合物[25].根據圖5可知,TPN的max值最高是主要的熒光物質,且在初始pH值實驗組的變化趨勢與PN濃度變化幾乎一致,因此TPN可以被檸檬酸污泥堿性厭氧發(fā)酵產酸過程利用.而在恒定pH值的實驗組尤其是C-pH=11和C-pH=12實驗組的TPN變化趨勢與PN濃度變化不同,可能因為發(fā)酵過程中HA和FA的大量溶出對PN測定產生干擾,同時FA和HA已被證實無法通過微生物分解產生VFAs[26],因此FA和HA的大量溶出會降低產酸效率[27-28],與VFAs的濃度降低相符.

圖4 堿性厭氧發(fā)酵液的熒光組分

圖5 堿性厭氧發(fā)酵液熒光組分Fmax的變化

2.2.4 厭氧發(fā)酵前后微生物群落的變化 由pH=10發(fā)酵前后(0和8d)微生物豐度和多樣性的變化結果(表1)可知,厭氧發(fā)酵后OUT指數、ACE指數、Chao指數和Shannon指數都明顯降低,表明堿性厭氧發(fā)酵產酸的菌群多樣性明顯低于初始污泥的多樣性.這一現象在屬(圖6b)水平上尤為明顯,如菌屬消失,以及vadinHA17和SBR1031*等菌屬的大量增加.其中是蛋白質降解厭氧菌[29],其消失可能與發(fā)酵后其PN含量降低有關;而HA17*菌屬[30]能夠利用葡萄糖產生乙酸鹽、丙酸鹽和氫氣[30]屬于產乙酸菌,有利于增加乙酸含量;菌屬[31]具有長鏈脂肪酸(C4及以上)降解功能,降低丁酸、戊酸等長鏈脂肪酸在總VFAs中占比;SBR1031*菌屬可代謝NH3-N[32],與發(fā)酵罐中的NH3-N含量變化有關.

表1 微生物群落豐度和多樣性變化

注:OTU是操作分類單位,Coverage反應測序深度指數,數值高于0.99表明測序深度足夠,結果可靠;ACE和Chao指數代表微生物豐度,數值越高豐度越高;Shannon和Simpson指數為香濃指數和辛普森指數,代表微生物多樣性,Shannon指數越高,多樣性越高,Simpson指數則相反.

圖6 門、屬水平上的物種相對豐度

*表示沒有明確的分類信息或分類名稱

基于樣品OTUs的注釋結果,門水平和屬水平微生物相對豐度如圖6所示,主要優(yōu)勢菌門為Firmicutes, Actinobacteriota, Bacteroidota, Proteobacteria, Chloroflexi,屬于污泥堿性發(fā)酵的優(yōu)勢菌群[33],但檸檬酸污泥堿性厭氧發(fā)酵過程改變了初始環(huán)境特征菌群的相對豐度.Firmicutes具有厚厚的細胞壁能夠在不同的污泥處理(例如加熱、堿化、酸化)中存活,含有多種產乙酸菌,可將多種VFAs代謝成乙酸、H2和CO2[34-35], Actinobacteriota中的細菌能降解多糖生成單糖和VFAs[36],然而發(fā)酵后Firmicutes和Actinobacteriota相對豐度分別由28.37%、21.58%降至10.15%、14.56%,可能是兩者菌門中不適于堿性厭氧環(huán)境下的劣勢菌種被淘汰所致[37-38].而Chloroflexi和Bacteroidota相對豐度分別由9.52%、10.87%增加至16.84%、14.39%,這是因為Chloroflexi菌門的微生物主要代謝碳水化合物,促進VFAs底物降解[39], Bacteroidota的微生物可分泌多種細胞外水解酶,將葡萄糖、纖維二糖、淀粉等物質轉化為乙酸、丁酸、異戊酸、H2和CO2[37,40],這兩種菌門中多種微生物適應堿性厭氧環(huán)境,有助于促進有機物的水解和VFAs的產生.同時發(fā)現部分非優(yōu)勢菌種Desulfobacterota、Thermotogota等相對豐度增加,據報道,Thermotogae菌群可以降解復雜的有機物,如木糖和纖維素等[41]. Desulfobacterota的部分菌群在厭氧條件下還原硫酸鹽,競爭NO2-電子供體,抑制NO2-還原產生N2O的反硝化過程[42],與氮含量變化有關.

2.3 堿性厭氧產酸發(fā)酵液外源碳源利用潛力分析

2.3.1 污泥脫水性能分析 如圖7(a)所示,堿處理和厭氧發(fā)酵導致CST增大,是因為OH-與金屬鹽離子聚集、發(fā)酵過程釋放的磷形成的化合物[43]以及上清液有機質含量增加等因素使大量水分被聚合,導致污泥過濾性能變差,這與Chen等[9]得出的酸性厭氧發(fā)酵可提高污泥的脫水能力結論一致.但OH-與鹽離子聚集以及VFAs產生的H+中和負電離子會降低Zeta電位絕對值(圖7b),甚至在pH=10的實驗組出現正電位,為維持強堿性環(huán)境的C-pH=11和C-pH=12實驗組,不斷引入OH-,與鹽離子和H+全部反應后仍有大量OH-游離,導致Zeta電位絕對值進一步增大,干擾污泥絮體聚集進一步增加CST.因而pH=10的實驗組脫水性能相對較好.由圖7(c)可以看出,堿性厭氧發(fā)酵可以降低污泥表觀黏度,因為在發(fā)酵過程中大分子有機質被降解為小分子物質,網絡結構被破壞內部阻力降低[44],這與Zhang等[45]和Zhang等[46]對市政污泥厭氧發(fā)酵對污泥脫水性能的影響研究得出的堿性厭氧發(fā)酵可以增強污泥流動性,降低污泥表觀黏度結論一致.因此可以考慮從流變方面對發(fā)酵后污泥進行脫水研究.

2.3.2 發(fā)酵液N、P的變化 使用厭氧產酸發(fā)酵液作為碳源時,還需要考慮發(fā)酵液中氮磷含量的影響.由圖8(a)可知,pH值不影響NH3-N的變化(0d),在發(fā)酵過程PN水解生成的氨基酸分子被厭氧菌利用時會生成游離態(tài)的NH3-N[1],使發(fā)酵后NH3-N濃度升高,因而代謝NH3-N的SBR1031*菌屬相對豐度升高.由于厭氧發(fā)酵無法完成硝化反硝化作用[47],且抑制反硝化過程相關的Desulfobacterota菌門相對豐度升高,使得NH3-N含量不斷升高.然而從圖8(b)可知pH值會影響TP的變化(0d),當pH311時TP濃度明顯升高,因為無機磷酸鹽類在pH311時不能穩(wěn)定存在[43],而這種高pH值導致的磷的釋放是可逆[48],在初始pH值實驗組中由于VFAs的產生降低pH值使無機磷酸鹽類重新沉淀,因此初始pH值的實驗組在8d時的TP濃度小于恒定pH實驗組,尤其是pH=10的處理組TP幾乎無明顯變化.

總體而言,污泥堿性厭氧發(fā)酵在增大污泥脫水難度的同時使得大量氨氮和可溶性磷釋放到發(fā)酵上清液中,已有研究表明[9,49],同時添加KH2PO4和MgCl2,可以在去除N、P的同時(NH3-N去除率>75%,TP去除率>80%)提高發(fā)酵后污泥的脫水能力,但藥劑添加會導致成本增加,影響污泥發(fā)酵產酸再利用的經濟性.

圖8 厭氧發(fā)酵前后發(fā)酵液NH3-N、TP的變化

3 結論

3.1 在初始pH=5～9的條件有利于檸檬酸剩余污泥厭氧發(fā)酵產甲烷,其中Control組累計甲烷產量最大為(40.25±2.86) mL/g VS,在初始和恒定pH310的堿性條件下,厭氧發(fā)酵易產生VFAs,同時更易于PN、PS的釋放.在恒定pH值實驗組,難分解的HA和FA會大量溶出不利于VFAs的產生.

3.2 初始pH=10的條件是檸檬酸剩余污泥厭氧產酸最佳的條件,發(fā)酵后產酸功能菌Chloroflexi、Bacteroidota的相對豐度分別由初始的9.52%、10.87%增至16.84%、14.39%,發(fā)酵4d的VFAs= (6681.47±126.82) mg COD/L濃度最高,是文獻報道中市政污泥產酸量的近2倍,此時乙酸為總VFAs的49.8%,有很大的碳源利用潛力.

3.3 堿性厭氧發(fā)酵過程中鹽離子的聚集和有機質的增加惡化污泥脫水性能,同時還增加N、P等物質的溶出,不利于發(fā)酵液作為外源碳源,因此針對發(fā)酵液用于污水處理的外部碳源,需要進一步了解污泥堿性發(fā)酵過程的SCOD、N、P變化規(guī)律和發(fā)酵液的性質,以便發(fā)現在提高N、P去除率的同時,還能改善發(fā)酵后污泥脫水性能的成本低、操作簡單的方法.

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Effect of pH on acid production by anaerobic fermentation of citric acid sludge and carbon source potential of fermentation broth.

SUN Dong-xia1, ZHOU Zi-an1, FENG Zhi-he2, HU Xiu-yu2, QI Guang-xia1, DONG Li-ming1*

(1.Key Laboratory of Cleaner Production and Integrated Resource Utilization of China National Light Industry, State Environmental Protection Key Laboratory of Food Chain Pollution Control, Beijing Technology and Business University, Beijing 100048, China；2.China Biotech Fermentation Industry Association, Beijing 100083, China)., 2022,42(11)：5198～5207

The research of acid production by anaerobic fermentation with different pH control conditions was carried out for the treatment of waste activated sludge from citric acid wastewater, using anaerobic granular sludge of citric acid wastewater as inoculum. The mechanism of anaerobic acid production of citric acid sludge was evaluated by the analysis of volatile fatty acids (VFAs), organic matter, nitrogen and phosphorus contents and sludge dewatering performance. The results showed that the alkaline conditions with pH310 were more conducive to the dissolution of organic matter to promote the production of VFAs. It was obvious that humic acid (HA) and fulvic acid (FA) at constant pH conditions would be dissolved in large quantities with Three-dimensional Excitation-Emission-Matrix Spectra analysis, thus reducing the yield of VFAs. The initial pH=10 was the optimum pH value for anaerobic acid production of citric acid sludge, and the VFAs concentration of (6681.47±126.82) mg COD/L for 4 days was the highest, which was nearly 2 times that of municipal sludge acid production reported in the literature, among which acetic acid was 49.8%. After fermentation, the relative abundances of acid-producing functional bacteria Chloroflexi and Bacteroidota increased from initial 9.52% and 10.87% to 16.84% and 14.39%, respectively. The normalized capillary suction time (CST) value of the final sludge was (11.34±0.27) s·L/g with good dewatering performance, and the TP concentration of fermentation broth was (20.45±0.33) mg/L. Studies have shown that the alkaline anaerobic fermentation of citric acid waste activated sludge to produce acid fermentation broth has a good development potential as an exogenous carbon source in the sewage treatment process.

pH value；citric acid waste activated sludge；alkaline anaerobic fermentation；volatile fatty acids；sludge dewatering performance

X705

A

1000-6923(2022)11-5198-10

孫東霞(1996-),女,山東德州人,北京工商大學碩士研究生,主要從事清潔生產與資源綜合利用研究.發(fā)表論文1篇.

2022-04-06

國家自然科學基金資助項目(41861124004)

* 責任作者, 教授, donglm@btbu.edu.cn