應用類神經網路推估二維徑向收斂流場追蹤劑試驗之延散度

Abstract

移流－延散方程式（advection-dispersion equation, ADE）為描述含水層污染溶質傳輸歷程之控制方程式，其中延散度（dispersivity）為模擬污染溶質傳輸主要傳輸參數。傳統上，以標準曲線套配法（type curve-fitting）套配現地追蹤劑試驗數據推估延散度需花費大量時間，且套配精確度不易掌握，故本研究應用倒傳遞類神經網路（back propagation neural network, BPN）結合二維徑向收斂流場追蹤劑試驗數學模式（scale-dependent dispersivity model, SDM），建立二維徑向收斂流場追蹤劑試驗套配模式（back propagation neural network fitting model, BPNFM），以提高推估延散度之精確度與效率。套配模式在訓練與驗證樣本之輸出誤差顯示，尺度縱向延散度套配模式在Peclet number介於0.5至100及有效孔隙率套配模式在有效孔隙率介於0.05至0.5之範圍推估誤差可保持在2%以內。而尺度側向延散度套配模式在尺度側向延散度介於0.3至10公尺之推估誤差為5%以內，在介於0.1至0.3公尺之推估誤差為8%以內，在介於0.03至0.1公尺之推估誤差為10%以內，在介於0.01至0.0.3公尺之推估誤差則為20%以內，各套配模式在其適用範圍內均可獲致良好之輸出精確度。在鹽寮核四廠址與假想追蹤劑試驗之數據套配結果顯示，二維徑向收斂流場追蹤劑試驗套配模式與標準曲線套配法在不同試驗場址之套配精確度相近。而套配效率上，二維徑向收斂流場追蹤劑試驗套配模式可大幅縮短標準曲線套配法套配過程花費之時間，因此二維徑向收斂流場追蹤劑試驗套配模式可在具備套配精確度下有效率地套配現地試驗數據，獲致可靠之延散度參數。

Advection-dispersion equation (ADE) describes the solute transport process in saturated aquifer, the dispersivity is the main parameter of ADE. Traditionally, the use of type curve-fitting to estimate dispersivity by analyzing the field data generally requires to a large amount of time, and the analysis accuracy is difficult to control. This study applied the back propagation neural network (BPN) model to analyze two-dimensional radially convergent flow tracer tests. The developed back propagation neural network fitting model (BPNFM) incorporates the scale-dependent dispersivity model (SDM) to automatically estimate the longitudinal and transverse dispersivities as well as the effective porosity. The prediction errors of training and validation data show that the scale-dependent longitudinal dispersivity fitting model and the effective porosity fitting model can maintain the prediction errors within 2% while the Peclet number is between 0.5 to 100, the effective porosity is between 0.05 to 0.5, respectively. The scale-dependent transverse dispersivity fitting model can maintain the prediction errors within 5%, 8%, 10% and 20% while the scale-dependent transverse dispersivity is between 0.3 to 10 meters, 0.1 to 0.3 meters, 0.03 to 0.1 meters and 0.01 to 0.3 meters, respectively. Two field data were used to demonstrate the efficiency and accuracy of BPNFM. The BPNFM not only significantly reduces the analysis time but also yields accurate matching result by comparing to the manual type curve-fitting results. The developed BPNFM is an effective tool for analyzing the dispersivities of the field tracer tests.