Numerical code (Python) for transient analysis of step-drawdown test

This program (TASHAn, Transient Analysis Step-drawdown test by Hyowon An) was developed for the interpretation of the step-drawdown test data. This program was created using Python. You can download the software from https://www.python.org/. This program was developed to calculate hydraulic parameters (T, r2S, P, C, a, RMSE) of the transient step-drawdown test. (T: aquifer transmissivity, r: well radius, S: aquifer storativity, P: well loss power, C: well loss coefficient, a: transient well loss shape factor.) Governing equations explaining T, r, S, P and C can be found from previous studies including Jacob (1947). For more information of transient well loss shape factor, please contact [e-mail]. This datasets include three files (input.xlsx, TASHAn.py, output.xlsx). The data in the input.xlsx was referred from Clark (1977). Description of each file is as follows: 1. input.xlsx 1) The 'input.xlsx' includes observed drawdowns[m], elapsed time[min] from the start of step-drawdown test, the number of total test steps[-] and pumping rate[m3/day] for each step. For example, the column 'B' indicates the elapsed time during the first step of the step-drawdown test and the column 'C' is for the observed drawdown during step 1. Column 'D' and 'E' are reserved for the elapsed time and drawdowns during the step 2. 2) The cell 'P1' is for assigning the number of total steps of the test and the cell 'P2~P7' is for assigning the average pumping rate for each step. 3) This version of code can evaluate the step-drawdown test with the maximum step number of six. If you have test data with five steps, you can leave as blank for the column 'L' and 'M'. 4) If the step-drawdown test includes some bad data and 'null' data, please fill these cells with value of zero '0'. Then, the code automatically skips these values. If you fill any cells outside the black line, the code could have errors. 2. TASHAn.py 1) If you had to install Python or Editor, run it and load the source code (TASHAn.py) 2) There are several modules included in this Code (numpy, lnfit and openpyxl). You can install these modules before running the code. 3) For the parameter optimization, this code uses iterative solver. Therefore, the ranges and initial values for each parameter should be assigned before running the model. If you wish to adjust these parameters, you can revise them in the source code ('line 346 ~ 349'.). If the initial values of the model is too high or low, the analysis result could be unreasonable. *When you running the 'TASHAn.py', the 'input.xlsx' and 'output.xlsx' must be closed. 3. output.xlsx If you can change the file name in 'line 399' Reference. Clark L (1977) The analysis and planning of step drawdown tests, Q J Eng Geol Hydrogeol. 10(2):125-143 Jacob CE (1947) Drawdown test to determine effective radius of artesian well, Trans Am Soc Civ Eng. 112(1):1047-1064

本程序（TASHAn，即由安孝元（Hyowon An）开发的瞬态分析阶梯降深试验程序）专为阶梯降深试验数据的解释而开发。本程序采用Python语言编写，可从https://www.python.org/下载Python运行环境。本程序用于计算瞬态阶梯降深试验的水力参数（T、r²S、P、C、a、RMSE），其中：T为含水层导水系数（aquifer transmissivity），r为井半径（well radius），S为含水层储水系数（aquifer storativity），P为井损功率（well loss power），C为井损系数（well loss coefficient），a为瞬态井损形状因子（transient well loss shape factor），RMSE为均方根误差（Root Mean Square Error）。阐释上述参数的控制方程可参考Jacob（1947）等既往研究。如需了解瞬态井损形状因子的更多细节，请联系邮箱[e-mail]。

本数据集包含三个文件：input.xlsx、TASHAn.py与output.xlsx。input.xlsx中的试验数据参考自Clark（1977）的研究。各文件详细说明如下：

1. input.xlsx
1) 该文件包含观测降深（单位：m）、阶梯降深试验启动后的历时（单位：min）、总试验步数（无量纲）以及各试验步骤的抽水速率（单位：m³/天）。例如，B列代表阶梯降深试验第一步骤的历时，C列对应第一步骤的观测降深；D列与E列为第二步骤的历时与观测降深数据。
2) 单元格P1用于填写试验总步数，单元格P2~P7用于填写各试验步骤的平均抽水速率。
3) 本版本代码最多可处理包含6个试验步骤的阶梯降深分析。若您的试验数据仅包含5个步骤，可将L列与M列留空。
4) 若阶梯降深试验数据存在无效或空值，请将对应单元格填充为0，代码将自动跳过此类数值。若在黑色边框外的单元格填充数据，可能导致代码运行出错。

2. TASHAn.py
1) 若您尚未安装Python或代码编辑器，请先完成安装，随后运行并加载本源代码（TASHAn.py）。
2) 本代码依赖numpy、lnfit与openpyxl三个第三方模块，请在运行代码前完成这些模块的安装。
3) 本代码采用迭代求解器进行参数优化，因此需在运行模型前为各参数设定取值范围与初始值。如需调整此类参数，可在源代码第346至349行进行修改。若模型初始值设置过高或过低，分析结果可能出现不合理偏差。
* 运行TASHAn.py时，请确保input.xlsx与output.xlsx处于关闭状态。

3. output.xlsx
您可在源代码第399行修改该输出文件的文件名。

参考文献：
1. Clark L. 阶梯降深试验的分析与规划[J]. 工程地质与水文地质季刊, 1977, 10(2):125-143.
2. Jacob CE. 测定自流井有效半径的降深试验[J]. 美国土木工程师学会会刊, 1947, 112(1):1047-1064.