抽水井群最佳操作優選模式之建立與應用

Abstract

本研究發展一盆地抽水井群最佳操作優選模式，為因應盆地之水文地質條件，以逐年計算之豐水期地下水位作為限制探討盆地之最大可抽水量，研究流程共分三個步驟：(1)地下水流模擬模式之建立；(2)類神經網路模擬觀測站地下水位模式之建立；(3)抽水井群最佳操作優選模式之建立。本研究首先根據研究區域之水文地質特性，採用MODFLOW地下水流模擬模式以模擬研究區域之地下水流，待率定地下水流模擬模式後，再以亂數產生抽水量以訓練三種不同之類神經網路，並採用井群分組與開關之二向變數以模擬井群實際之管理操作，本研究共發展二套優選模式，分別為井群抽水最大化優選模式及月穩定需水量最大化優選模式，其中前者之目標函數為井群抽水量最大化，限制式則為抽水能力限制、抽水井群開關限制、豐水期地下水位限制與類神經網路模擬地下水位模式之限制，因為本優選問題屬於混合整數非線性規劃(MINLP)，且含有大量之限制式，無法採用啟發式演算法協助求解，故採用Lingo套裝軟體求取最佳解。 本研究將所發展之抽水井群最佳操作優選模式應用於濁水溪中游之名竹盆地，測試不同架構之類神經網路與隱藏神經元個數後，可得前饋式類神經網路及10個隱藏層神經元最可代表研究區域內各觀測站之地下水位變化，優選模式以Lingo套裝軟體求解而得井群操作之最佳解，其結果顯示隨著名竹盆地抽水井群之分組從1組增加至4組，抽水量亦會增加達8成；此外豐水期之水位回復比例越高，則井群之可抽水量越低，月穩定需水量最大化優選模式之最佳抽水量稍小於井群抽水最大化優選模式之最佳抽水量，為驗證優選模式之地下水位變動是否合理，本研究將最佳解之井群抽水量代入MODFLOW地下水模擬模式，驗證結果顯示MODFLOW所模擬之豐水期地下水位皆符合限制式之水位，因此本優選模式所求得之井群操作結果近似於全域最佳解。

The study is to develop an optimization model for the pumping well group, which can be used to determine the maximum pumping rate under the limitation of groundwater level. The flow chart of this study can be divided into three procedures, which are (1) the development of groundwater simulation model for the study area; (2) the training of the artificial neural networks model and (3) the development of optimization model for the optimal operation of pumping well groups. The study first investigates the hydrological and geophysical characteristics of the study area. After the calibration of the groundwater simulation model is completed, three different artificial neural networks, feed forward neural network, radial basis neural network and linear layer neural network, are trained by random pumping rates generated by MODFLOW to determine which ANN is the most suitable to simulate the groundwater level of the observation station in the study area. The optimization model of the optimal operation for the pumping well group is developed. The objective function is to maximize the pumping rates of the well groups under the constraints of the maximum pumping rate of each well, the simulation of groundwater level at the observation well by ANN model, the limit of groundwater level during wet period and the on-off switch of each well group. Because the optimization problem developed by the study belongs to mixed integer nonlinear programming (MINLP), which contains large quantities of constraints, Lingo software is applied to obtain the optimal solution of the optimization problem. The methodology developed by this study is applied to Ming-Chu Basin. After training process and validation, the feed forward artificial neural network is the most suitable tool to represent the groundwater fluctuation of the observation well in the study area. The optimization model developed for Ming-Chu Basin is solved by Lingo software. The results show with increasing the division of well groups from 1 to 4 groups, the optimal pumping rates will be increased by nearly 80%. However, with increasing the recovery rate of groundwater level during wet period, the optimal pumping rate will be decreased accordingly. The optimal pumping rate is simulated by MODFLOW to validate the requirement of groundwater level during wet periods is fulfilled. The results show that the groundwater level of the optimal pumping rate simulated by MODFLOW is above or near the required groundwater level specified by the constraints. Therefore, the optimal pumping rate can be considered as the global optimal approximate solution of the optimization model.