復雜DNAPL污染源區(qū)溶解相污染通量的升尺度計算

宋美鈺,施小清,馬春龍,康學遠,杜方舟

復雜DNAPL污染源區(qū)溶解相污染通量的升尺度計算

宋美鈺,施小清*,馬春龍,康學遠,杜方舟

(南京大學地球科學與工程學院,表生地球化學教育部重點試驗室,江蘇 南京 210023)

重非水相液體(DNAPL)污染場地中NAPL相污染物會持續(xù)溶解于地下水中,釋放出溶解相污染羽,對人體健康產(chǎn)生威脅.準確評估DNAPL污染場地源區(qū)下游的溶解相污染通量至關(guān)重要.由于介質(zhì)的非均質(zhì)性常形成復雜DNAPL污染源區(qū),其溶解相污染通量往往呈現(xiàn)出階段性變化.目前溶解相污染通量計算普遍采用Christ等提出的雙域升尺度模型,但該模型僅適用于弱非均質(zhì)性的污染源區(qū).本文基于大量強非均質(zhì)性條件下的污染源區(qū)數(shù)值算例,修正了Christ雙域模型中污染源區(qū)衰減指數(shù)的經(jīng)驗公式,將該模型的適用范圍推廣至強非均質(zhì)性的復雜污染源區(qū).通過蒙特卡羅數(shù)值算例及兩個二維砂箱試驗數(shù)據(jù)驗證了修正模型的適用性和精度.對比結(jié)果表明:修正模型可廣泛適用于不同結(jié)構(gòu)的復雜DNAPL污染源區(qū),與以往的計算方法相比,修正模型計算的溶解相污染通量精度提高了約35%.

重非水相液體；溶解相污染通量；離散狀和池狀結(jié)構(gòu)的質(zhì)量比；污染源區(qū)衰減；升尺度模型

隨著有機化工業(yè)的不斷發(fā)展,重非水相液體(DNAPL)污染問題日趨嚴重[1-2].由于具有密度大、粘滯度低、溶解度低等特點,從地表泄漏的DNAPL在重力和毛細管力的共同作用下,穿過包氣帶向含水層底部遷移,最終以連續(xù)的池狀結(jié)構(gòu)在低滲透地層上聚集[3].在此過程中,部分DNAPL殘留在多孔介質(zhì)的孔隙中,呈現(xiàn)不連續(xù)的離散狀結(jié)構(gòu)[4].池狀和離散狀結(jié)構(gòu)的DNAPL均以自由非水相的形式存在,其所在區(qū)域被定義為DNAPL污染源區(qū)[5].為了表征DNAPL污染源區(qū)常常采用離散狀和池狀DNAPL的質(zhì)量比(GTP)來刻畫污染源區(qū)的結(jié)構(gòu),因此可將DNAPL污染源區(qū)劃分為離散狀污染源區(qū)(GTP>1)和池狀污染源區(qū)(GTP<1)[6-8].隨著地下水的流動,不同結(jié)構(gòu)的污染源區(qū)緩慢地溶解于水中,沿地下水流方向形成溶解羽,長期威脅人類的健康.

近年來,DNAPL污染源區(qū)的復雜溶解行為吸引了越來越多的學者關(guān)注[9-10].目前地下水環(huán)境管理一般采用污染物濃度限值標準[11],但由于DNAPL在地下不同區(qū)域的分布并不均勻,僅用濃度標準無法準確評估污染源區(qū)的風險并制定合理的修復方案[12].因此,有學者提出了污染通量概念,即地下水下游某監(jiān)測斷面單位時間單位面積的污染物質(zhì)量.近些年來,管理機構(gòu)逐漸達成共識,認為污染通量比濃度能提供更準確的場地污染情況,從而幫助管理者合理評估污染源區(qū)的自然衰減程度并制定修復方案[13-14].溶解相污染通量的常用計算方法包括:斷面監(jiān)測法、井捕獲法、被動式通量計法、等值線估測法以及溶質(zhì)運移模型法[12],其中前三類方法因為需要采用侵入性手段進行輔助,因此具有實施難度大、周期長、成本高等問題,而等值線估測法的適用范圍有限.因此溶質(zhì)運移模型以非侵入性、適用范圍廣、可預測等特點得到了越來越多的關(guān)注.采用該方法計算溶解相污染通量時,需要精細刻畫污染源區(qū)的結(jié)構(gòu)作為驅(qū)動數(shù)據(jù),進而基于多相流模型求解[15-16].但實際場地的污染源區(qū)精細刻畫難度很大,需要布設很多監(jiān)測點,因此耗費大量的人力、物力、財力,并且多相流模型計算成本較高,所以導致該方法的工作量較大.

除此之外,精細刻畫含水層非均質(zhì)性以及復雜污染源區(qū)的方法僅在小尺度范圍內(nèi)有效,對于大多數(shù)中等尺度(上百米)場地的羽狀污染都不可行,由于參數(shù)測量尺度和研究區(qū)域尺度之間的巨大差異以及含水層的空間非均質(zhì)性,有必要對參數(shù)進行升尺度轉(zhuǎn)換,將精細測量尺度內(nèi)收集的數(shù)據(jù)信息轉(zhuǎn)換為較粗計算尺度下的相關(guān)信息,以滿足大尺度建模要求[17].因此在估算溶解相污染通量時,為了解決上述問題并減少工作量,升尺度計算方法得到不斷發(fā)展,學者們重點關(guān)注溶解相污染通量隨污染源區(qū)衰減過程的變化,嘗試用少量的等效參數(shù)來刻畫污染源區(qū)和含水層的非均質(zhì)性,以期在較粗的尺度上準確計算污染通量,由此建立以下兩類模型.

在上述兩類模型中,溶解相污染通量隨污染源區(qū)衰減過程的變化均是通過一個常數(shù)參數(shù)表征.然而對于實際的場地,污染源區(qū)結(jié)構(gòu)往往較為復雜,隨著溶解的不斷進行,溶解相污染通量呈現(xiàn)明顯的階段性變化,往往難以用一個常數(shù)來刻畫[24].

1 研究方法

1.1 控制方程

假定在飽和含水層中存在一個復雜的DNAPL污染源區(qū)(圖1),該源區(qū)由多個離散狀污染源區(qū)和池狀污染源區(qū)共同構(gòu)成.污染源區(qū)內(nèi)污染物的飽和度均大于零.連續(xù)的池狀DNAPL和不連續(xù)的離散狀DNAPL在地下水中緩慢地溶解,在水流方向形成溶解羽.假設忽略生物降解、揮發(fā)及吸附帶來的影響,基于溶質(zhì)運移模型,DNAPL的溶解過程可以通過式(1)表示.求解式(1)可量化在地下水中溶解相DNAPL的濃度,將其與地下水流速相乘,計算DNAPL污染源區(qū)的溶解相污染通量.

圖1 DNAPL污染源區(qū)示意

1.2 升尺度模型

升尺度計算方法對于觀測數(shù)據(jù)需求少、計算效率高,其基本思路是通過采用少量的等效參數(shù)來刻畫污染源區(qū)和含水層的非均質(zhì)性,在較粗的尺度上計算污染通量.升尺度模型的建立一般需基于下述假設[21]:

(2)忽略橫向彌散和分子擴散的影響.

(4)污染物飽和度發(fā)生變化的時間極短,且地下水的流速基本保持不變,溶解動力學極為接近穩(wěn)定狀態(tài),因此將溶解過程視為擬穩(wěn)態(tài)的.

由此可將式(1)簡化為以下的升尺度計算模型[19]:

1.3 升尺度模型參數(shù)的擬合

數(shù)值計算過程中對空間和時間變量分別進行離散.在空間上,將污染源區(qū)離散為個單元(為整數(shù)且31),其衰減過程的計算從污染源區(qū)上游單元向下游單元過渡;在時間上,將污染源區(qū)的總時長離散為個相等步長(為整數(shù)且31,>0),且假設在每個步長內(nèi),溶解過程均處于穩(wěn)定狀態(tài),飽和度和等效滲透系數(shù)等污染源區(qū)相關(guān)參數(shù)保持不變.在此基礎(chǔ)上,基于以下步驟模擬污染源區(qū)的衰減:

(4)重復步驟(2)、(3)直至污染源區(qū)耗竭.

表1 模型參數(shù)設置

圖2 GTP =6.6時DNAPL的初始飽和度

圖3 GTP =6.6時污染源區(qū)通量加權(quán)濃度擬合情況

對比不同的時間步長離散

圖4 β和GTP的擬合情況

Fig.4 Fitting results of β and GTP

圖5 GF和1-M/M0的擬合情況

其中

2 驗證

2.1 采用蒙特卡洛數(shù)值試驗驗證

由于單個實現(xiàn)需耗時1～3h,為避免過大的計算量,本文僅選取100個污染源區(qū),分別采用式(15)中的解析解和數(shù)值計算方法對通量加權(quán)濃度進行計算,并統(tǒng)計二者間的RMSE.由圖6可知,對于84%的污染源區(qū),通量加權(quán)濃度的RMSE分布在160mg/L以內(nèi),RMSE的最大值為208.05mg/L.與此同時,分別采用Zhu-Sykes模型、Parker-Park模型以及Christ雙域模型計算上述100個污染源區(qū)的通量加權(quán)濃度[18,21,29].經(jīng)過與數(shù)值計算方法所得結(jié)果對比發(fā)現(xiàn),前兩類模型計算得到的RMSE的平均值分別為201.37和492.41mg/L.與這兩類模型相比,本文拓展的解析解計算精度平均提高了約10%和35%.而與Christ雙域模型相比,本文拓展的解析解在大約前40%～60%衰減過程中可以更準確地推估溶解相污染通量,其精度平均提高了約4%.

為了更直觀地驗證解析解對于污染源區(qū)衰減過程中多階段溶解相污染通量的計算能力,本文展示了其中9個污染源區(qū)通量加權(quán)濃度的擬合情況.由圖7可知,采用式(15)解析解計算的結(jié)果與數(shù)值計算的結(jié)果在不同結(jié)構(gòu)的復雜污染源區(qū)的算例中均能較好地擬合,相比于Zhu-Sykes模型、Parker-Park模型以及Christ雙域模型[18,21,29],可以更準確地刻畫溶解相污染通量的階段變化.由上述結(jié)果可見本文拓展的解析解可以廣泛適用于強非均質(zhì)性的復雜DNAPL污染源區(qū)的階段變化的溶解過程.

圖6 通量加權(quán)濃度均方根誤差的頻率直方圖

圖7 污染源區(qū)衰減過程中通量加權(quán)濃度的擬合情況

2.2 采用砂箱試驗驗證

表2 試驗參數(shù)設置[37]

2.2.1 均質(zhì)介質(zhì)中的單個DNAPL污染源區(qū) 為了達到均質(zhì)介質(zhì)的背景條件,DiFilippo等在砂箱中填入大小為40/50目且均勻分布的砂[37],并在底部布設2cm厚的70/100目的細砂,以形成低滲透性的邊界,便于DNAPL以池狀結(jié)構(gòu)聚集.隨后在砂箱頂部釋放約12mL的TCE,形成一個中部為離散狀形態(tài),底部為池狀形態(tài)分布的復雜污染源區(qū)(圖8).污染源區(qū)穩(wěn)定后,從砂箱左側(cè)以恒定的速率注入去離子水,形成一個水力梯度約為0.01的流場,并在砂箱右側(cè)端口進行取樣分析,從而獲得各個時刻污染源區(qū)的通量加權(quán)濃度.試驗的具體設置見表2.

圖8 單個污染源區(qū)試驗的初始飽和度[37]

圖9 單個污染源區(qū)試驗和解析解的結(jié)果對比

由圖9可知,對于單個DNAPL污染源區(qū),采用本文拓展的解析解計算的結(jié)果能較好地擬合試驗結(jié)果.試驗值和解析解所得的計算值間的RMSE= 124.92mg/L.同樣采用Zhu-Sykes模型、Parker-Park模型和Christ雙域模型分別對通量加權(quán)濃度進行求解[18,21,29],經(jīng)過與數(shù)值計算方法所得結(jié)果對比發(fā)現(xiàn),前兩類模型計算得到的RMSE的平均值分別為167.42和437.25mg/L.與這兩類模型相比,本文拓展的解析解計算的精度約提高了10%和30%,并且可以更精確地刻畫出污染源區(qū)衰減過程中溶解相污染通量的階段變化.而與Christ雙域模型相比,本文拓展的解析解在大約前60%衰減過程中可以更準確地推估溶解相污染通量,其精度提高了約3%.

圖10 多個污染源區(qū)試驗的初始飽和度[37]

采用本文基于雙域模型拓展的解析解計算污染源區(qū)衰減過程中的通量加權(quán)濃度,并將試驗結(jié)果與之對比.由圖11可知,對于多個DNAPL污染源區(qū),采用本文拓展后的解析解計算的結(jié)果與試驗結(jié)果擬合較好.試驗值和計算值間的RMSE=41.22mg/L,同樣采用Zhu-Sykes模型、Parker-Park模型和Christ雙域模型分別對通量加權(quán)濃度進行求解[18,21,29],經(jīng)過與數(shù)值計算方法所得結(jié)果對比發(fā)現(xiàn),前兩類模型計算得到的RMSE的平均值分別為309.43和200.97mg/L.與這兩類模型相比,本文基于雙域模型拓展的解析解計算的精度約提高了20%和15%,可以更精確地刻畫出污染源區(qū)衰減過程中溶解相污染通量的階段性變化.而與Christ雙域模型相比,本文拓展的解析解在大約前60%衰減過程中可以更準確地推估溶解相污染通量,其精度提高了約4%.

圖11 多個污染源區(qū)試驗和解析解的結(jié)果對比

3 結(jié)論

3.1 本文采用大量強非均質(zhì)性的復雜污染源區(qū)算例,修正了雙域模型中污染源區(qū)衰減指數(shù)的經(jīng)驗公式,將溶解相污染通量解析解的適用范圍推廣至強非均質(zhì)性的復雜污染源區(qū).

3.2 通過與蒙特卡洛數(shù)值計算結(jié)果對比驗證可知,本文基于雙域模型拓展的解析解可廣泛應用于強非均質(zhì)性的復雜DNAPL污染源區(qū),較以往模型相比,修正模型的精度提高約10%～35%.

3.3 通過與兩個砂箱試驗結(jié)果對比驗證可知,修正模型可以更精確地刻畫復雜DNAPL污染源區(qū)衰減過程中溶解相污染通量的階段性變化.本次研究的局限在于僅考慮溶解相的平衡溶解,后續(xù)可針對非平衡溶解過程,進一步提高污染源區(qū)衰減過程中溶解相污染通量的計算精度.

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Upscaling dissolved phase mass flux for complex DNAPL source zones.

SONG Mei-yu, SHI Xiao-qing*, MA Chun-long, KANG Xue-yuan, DU Fang-zhou

(Key Laboratory of Surficial Geochemistry, Ministry of Education, School of Earth Science and Engineering, Nanjing University, Nanjing 210023, China)., 2022,42(5)：2095～2104

The NAPL phase in the Dense Non-Aqueous Phase Liquid (DNAPL) contaminated site are dissolved in the flowing groundwater sustainably, thus a downstream contaminant plume is created, and a threat is posed to human health. It is important to accurately estimate the downstream contaminant mass flux from the DNAPL source zone. Due to the geological heterogeneity, the mass flux of dissolved phase is changed periodically. The dual-domain upscaling model developed by Christ et al. was often used to calculate the mass flux, however, it was only applicable to the DNAPL source zone with weak heterogeneity. Many numerical examples were used for complex DNAPL source zones with strong heterogeneity, to modify the empirical formula for deriving the source zone depletion index in the dual-domain model, thus the application scope of the dual-domain upscaling model were extended to strong heterogeneity. The applicability and accuracy of the modified model was validated based on Monte Carlo synthetical cases and two two-dimensional sandbox experiments. The comparison results showed that the modified model could be widely applied to complex DNAPL source zones with different structures. Compared with the previous, the accuracy of the mass flux calculated by the modified model was increased by about 35%.

DNAPL；mass flux；GTP；source zone depletion；upscaled models

X703.5

A

1000-6923(2022)05-2095-10

宋美鈺(1998-),女,遼寧大連人,南京大學碩士研究生,主要從事地下水數(shù)值模擬研究.

2021-09-22

國家重點研發(fā)計劃項目( 2018YFC1800604);國家自然科學基金資助項目(41977157)

* 責任作者, 教授, shixq@nju.edu.cn