An approach, based on FSRM and a fundamental solution of the groundwater transport equation, is proposed to recover the release history of a contaminant from a known source site. Case studies for the recovery of source release history are demonstrated for contaminant transport in a two-dimensional infinite aquifer system.
Three different source release functions, namely the exponential function, triangle function, and step functions are selected to evaluate the performance of FSRM in recovering the release history and other inverse methods such as SA, LS, BVLS, MRE, and TR. The FSRM can only analyze the uniformly distributed temporal concentration data; therefore, the cubic spline is applied to transform the nonuniform data into uniform ones in order to facilitate the use of FSRM in recovering the release history recovery.
The results obtained from the case studies in scenarios 1 and 2 indicate that the proposed approach perform reasonably well in recovering the release history. The following conclusions can be drawn from this study:
1. The proposed method, FSRM, is effective in recovering arbitrary source release history for contaminant transport in one-, two- and three-dimensional domains. Various source geometry and aquifer configuration can be considered if the fundamental solution is chosen from AT123D (Yeh, 1981).
2. Most of existing methods in recovering the release history of a contamination plume requires the use of spatial concentration data which in fact is very costly to obtain from many monitoring wells. In contrast, the FSRM is capable of recovering the release history from the temporal concentration data sampled from only one monitoring well. This implies that the FSRM is a cost-effective method in terms of the number of monitoring wells used in practical applications.
3. The recovered release history is generally sensitive to the measurement error.
However, the FSRM perform reasonably well in recovering the source release history if the regularization parameter r is properly chosen. According to this study, the appropriate value of r is 4 for the exponential source pattern and 5 for the release history in terms of triangle function or step function.
4. The FSRM is generally more effective than other existing methods such as SA, LS, BVLS, MRE, and TR in recovering the release histories for the triangle and step source release functions.
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Table 1 The mean and standard deviation of measurement error for different error level ε of three cases.
Exponential function (×10-3) Triangle function (×10-3) Step function (×10-3) Error level
* SDE = standard deviation
(a)
(b)
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FIGURE 1 The recovered source release history (a) exponential function for r = 3, 4, 5 (b) triangle function for r = 4, 5, 6 (c) step function for r = 4, 5, 6
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(b)
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FIGURE 2 The recovered source release history with time interval 1 day and 3 day (a) exponential function for r = 5 and r = 3 (b) triangle function for r = 5 and r = 4
(c) step function for r = 5 and r = 4
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(b)
(c)
FIGURE 3 Non-uniform observed data, interpolated data, cubic spline, and recovered source release history of (a) exponential function for r = 4
(b) triangle function for r = 5 (c) step function for r = 5
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(b)
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FIGURE 4 The observed data with measurement error ε = 0.01, 0.05, and 0.1 (a) exponential function (b) triangle function (c) step function
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FIGURE 5 The source release history with measurement error ε = 0.01, 0.05, and 0.1 (a) exponential function (b) triangle function (c) step function
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FIGURE 6 (a) SA method for triangle function source history solution (b) SA method for step function source history solution
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FIGURE 7 (a) MRE method for triangle function source history solution (b) MRE method for step function source history solution
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FIGURE 8 LS, BVLS and TR methods for source history solution (a) triangle function form (b) step function form
個人資料
姓名：王毓婷
生日：民國 72 年 5 月 27 日 出生地：彰化市
電話：0928976189
住址：苗栗縣通霄鎮通西里和平路 73 號
學歷：民國 94 年畢業於國立中山大學海洋環境及工程學系 民國 96 年畢業於國立交通大學環境工程研究所