雙區受壓含水層污染傳輸之半解析解與近似解

本研究發展一個數學模式用來描述徑向雙區受壓含水層系統中污染物的濃度分佈，含水層系統由膚層及主要含水層兩區域所構成。此模式包含兩個描述污染物濃度分佈之暫態控制方程式，一個用來描述膚層而另一個用來描述主要含水層。當污染物被連續定量的注入井中時，由於延散及流傳通量而在井壁處考慮為第三類 (Robin) 邊界條件。應用拉普拉斯轉換求得此模型的半解析解，並且當忽略膚層部分時可成功轉回單區的半解析解。此外，我們也根據相同的模型考慮污染物在離井一段距離後因為延散機制的影響變的很小的將其忽略的假設下發展出一個在時間域下的近似解。研究結果發現膚層的影響會隨著時間的增加而減少，此外由於井壁上的濃度在初期明顯地下降，所以若採用第一類 (Dirichlet) 邊界條件來描述濃度分佈會高估其在井壁上的濃度。由於近似解有著相較半解析解容易計算的優點，而且當時濃度預測能夠有著相當好的準確性，因此是一個用來進行風險評估時的良好工具。

關鍵字

徑向傳輸；第三類 (Robin) 邊界條件；膚層；拉普拉斯轉換；地下水污染

並列摘要

This study develops a mathematical model for contaminant transport due to well injection in a radial two-zone confined aquifer system, which is composed of a wellbore skin zone and a formation zone. The model contains two transient equations describing the contaminant concentration distributions; one is for contaminant transport in the skin zone while the other is for transport in the formation zone. The contaminants are injected into the well with given dispersive and advective fluxes; therefore, the well boundary is treated as a third-type (Robin) condition. The solution of the model derived by the method of Laplace transforms can reduce to a single-zone solution in the absence of the skin zone. In addition, an approximate solution in the time domain is also developed by neglecting dispersion for the case that the contaminants move away from the injection well. Analysis of the semi-analytical solution showed that the influence of the skin zone on the concentration distribution decreases as time elapses. The distribution will be over-estimated near the wellbore if the constant concentration (Dirichlet) condition is adopted at the well boundary. The approximate solution has advantages of easy computing and yield reasonable predictions for Peclet numbers larger than 50, and thus is a practical extension to existing methods for designing aquifer remediation systems or performing risk assessments.

並列關鍵字

radial transport ； Robin boundary condition ； skin zone ； Laplace transform ； roundwater pollution

參考文獻

Abramowitz, M., Stegun, I.A., 1972. Handbook of mathematical functions: with formulas, graphs, and mathematical tables. Dover, New York.

Bear, J., 1972. Dynamics of fluids in porous media. American Elsevier, New York.

Chen, C.S., 1987. Analytical solutions for radial dispersion with Cauchy boundary at injection well. Water Resour. Res., 23(7): 1217-1224.

Chen, J.S., 2010. Analytical model for fully three‐dimensional radial dispersion in a finite‐thickness aquifer. Hydrol. Process., 24(7): 934-945.

Chen, J.-S., Chen, J.-T., Liu, C.-W., Liang, C.-P., Lin, C.-W., 2011. Analytical solutions to two-dimensional advection–dispersion equation in cylindrical coordinates in finite domain subject to first-and third-type inlet boundary conditions. J. Hydrol., 405(3): 522-531.

國際替代計量

雙區受壓含水層污染傳輸之半解析解與近似解

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