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"cell_type": "markdown",
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"source": [
"# 3. Confined Aquifer Test - Sioux Flats"
]
},
{
"cell_type": "markdown",
"metadata": {
"editable": true,
"slideshow": {
"slide_type": ""
},
"tags": []
},
"source": [
"### Import packages"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"import pandas as pd\n",
"\n",
"import timflow.transient as tft\n",
"\n",
"plt.rcParams[\"figure.figsize\"] = (5, 3) # default figure size"
]
},
{
"cell_type": "markdown",
"metadata": {
"editable": true,
"slideshow": {
"slide_type": ""
},
"tags": []
},
"source": [
"### Introduction and Conceptual Model"
]
},
{
"cell_type": "markdown",
"metadata": {
"editable": true,
"slideshow": {
"slide_type": ""
},
"tags": []
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"source": [
"This example is a pumping test done in Sioux Flats, South Dakota, USA. The data comes from the AQTESOLV documentation (Duffield, 2007). \n",
"\n",
"The aquifer is 50 ft thick and is bounded by impermeable layers. The test was conducted for 2045 minutes (~34 hours), with a constant pumping rate of 2.7 ft$^3$/s. Drawdown data has been collected at three piezometers located 100, 200 and 400 ft away, respectively. The well radius is 0.5 ft. "
]
},
{
"cell_type": "markdown",
"metadata": {
"editable": true,
"slideshow": {
"slide_type": ""
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"tags": []
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"source": [
"![](\"./figs/Sioux.png\")
"
]
},
{
"cell_type": "markdown",
"metadata": {
"editable": true,
"slideshow": {
"slide_type": ""
},
"tags": []
},
"source": [
"### Load data"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [],
"source": [
"# time and drawdown of piezometer 100ft away from pumping well\n",
"data1 = np.loadtxt(\"data/sioux100.txt\")\n",
"t1 = data1[:, 0]\n",
"h1 = data1[:, 1]\n",
"\n",
"# time and drawdown of piezometer 200ft away from pumping well\n",
"data2 = np.loadtxt(\"data/sioux200.txt\")\n",
"t2 = data2[:, 0]\n",
"h2 = data2[:, 1]\n",
"\n",
"# time and drawdown of piezometer 300ft away from pumping well\n",
"data3 = np.loadtxt(\"data/sioux400.txt\")\n",
"t3 = data3[:, 0]\n",
"h3 = data3[:, 1]"
]
},
{
"cell_type": "markdown",
"metadata": {
"editable": true,
"slideshow": {
"slide_type": ""
},
"tags": []
},
"source": [
"### Parameters and model"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [],
"source": [
"# known parameters\n",
"Q = (\n",
" (2.7 * 0.3048**3) * 60 * 60 * 24\n",
") # constant discharge in m^3/d (2.7 ft^3/s = 6605.754 m^3/d)\n",
"b = 50 * 0.3048 # aquifer thickness in m (50 ft = 15.24 m)\n",
"rw = 0.5 * 0.3048 # well radius in m (0.5 ft = 0.1524 m)\n",
"r1 = 100 * 0.3048 # distance between obs1 to pumping well (100 ft = 30.48 m)\n",
"r2 = 200 * 0.3048 # distance between obs2 to pumping well (200 ft = 60.96 m)\n",
"r3 = 400 * 0.3048 # distance between obs3 to pumping well (400 ft = 121.92 m)"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"self.neq 1\n",
"solution complete\n"
]
}
],
"source": [
"# timflow model\n",
"ml = tft.ModelMaq(kaq=10, z=[0, -b], Saq=0.001, tmin=0.001, tmax=10, topboundary=\"conf\")\n",
"w = tft.Well(ml, xw=0, yw=0, rw=rw, tsandQ=[(0, Q)], layers=0)\n",
"ml.solve()"
]
},
{
"cell_type": "markdown",
"metadata": {
"editable": true,
"slideshow": {
"slide_type": ""
},
"tags": []
},
"source": [
"### Estimate aquifer parameters"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"...............................................\n",
"Fit succeeded.\n"
]
}
],
"source": [
"# unknown parameters: k, Saq\n",
"cal = tft.Calibrate(ml)\n",
"cal.set_parameter(name=\"kaq\", initial=10, layers=0)\n",
"cal.set_parameter(name=\"Saq\", initial=1e-4, layers=0)\n",
"cal.series(name=\"obs1\", x=r1, y=0, t=t1, h=h1, layer=0) # Adding well 1\n",
"cal.series(name=\"obs2\", x=r2, y=0, t=t2, h=h2, layer=0) # Adding well 2\n",
"cal.series(name=\"obs3\", x=r3, y=0, t=t3, h=h3, layer=0) # Adding well 3\n",
"cal.fit(report=False)"
]
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"
\n",
" \n",
" \n",
" | \n",
" optimal | \n",
"
\n",
" \n",
" \n",
" \n",
" | kaq_0_0 | \n",
" 282.795232 | \n",
"
\n",
" \n",
" | Saq_0_0 | \n",
" 0.004209 | \n",
"
\n",
" \n",
"
\n",
"
"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"hm1 = ml.head(r1, 0, t1)\n",
"hm2 = ml.head(r2, 0, t2)\n",
"hm3 = ml.head(r3, 0, t3)\n",
"plt.semilogx(t1, h1, \".\", label=\"obs1\")\n",
"plt.semilogx(t1, hm1[0], label=\"timflow result 1\")\n",
"plt.semilogx(t2, h2, \".\", label=\"obs2\")\n",
"plt.semilogx(t2, hm2[0], label=\"timflow result 2\")\n",
"plt.semilogx(t3, h3, \".\", label=\"obs3\")\n",
"plt.semilogx(t3, hm3[0], label=\"timflow result 3\")\n",
"plt.title(\"Model Results\")\n",
"plt.xlabel(\"time [d]\")\n",
"plt.ylabel(\"head change [m]\")\n",
"plt.legend()\n",
"plt.grid()"
]
},
{
"cell_type": "markdown",
"metadata": {
"editable": true,
"slideshow": {
"slide_type": ""
},
"tags": []
},
"source": [
"### Comparison of results\n",
"The performance of `timflow` is compared to the results based on Theis’ analytical solution (Theis, 1935), implemented in the software AQTESOLV (Duffield, 2007). \n",
"\n",
"`timflow` achieved similar results as AQTESOLV. "
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"editable": true,
"slideshow": {
"slide_type": ""
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"tags": [
"hide-input"
]
},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
" \n",
" \n",
" | | \n",
" k [m/d] | \n",
" Ss [1/m] | \n",
" RMSE [m] | \n",
"
\n",
" \n",
" \n",
" \n",
" | timflow | \n",
" 282.80 | \n",
" 4.21e-03 | \n",
" 0.004 | \n",
"
\n",
" \n",
" | AQTESOLV | \n",
" 282.66 | \n",
" 4.04e-03 | \n",
" - | \n",
"
\n",
" \n",
"
\n"
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"text/plain": [
""
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"execution_count": 17,
"metadata": {},
"output_type": "execute_result"
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"source": [
"t = pd.DataFrame(\n",
" columns=[\"k [m/d]\", \"Ss [1/m]\", \"RMSE [m]\"], index=[\"timflow\", \"AQTESOLV\"]\n",
")\n",
"\n",
"t.loc[\"timflow\"] = np.append(cal.parameters[\"optimal\"].values, cal.rmse())\n",
"t.loc[\"AQTESOLV\"] = [282.659, 4.0355e-03, \"-\"]\n",
"\n",
"t_formatted = t.style.format(\n",
" {\n",
" \"k [m/d]\": \"{:.2f}\",\n",
" \"Ss [1/m]\": \"{:.2e}\",\n",
" \"RMSE [m]\": lambda x: \"-\" if x == \"-\" else f\"{float(x):.3f}\",\n",
" }\n",
")\n",
"t_formatted"
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{
"cell_type": "markdown",
"metadata": {
"editable": true,
"slideshow": {
"slide_type": ""
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"tags": []
},
"source": [
"## References"
]
},
{
"cell_type": "markdown",
"metadata": {
"editable": true,
"slideshow": {
"slide_type": ""
},
"tags": []
},
"source": [
"* Duffield, G.M. (2007), AQTESOLV for Windows Version 4.5 User's Guide, HydroSOLVE, Inc., Reston, VA.\n",
"* Newville, M., Stensitzki, T., Allen, D.B., Ingargiola, A. (2014), LMFIT: Non Linear Least-Squares Minimization and Curve Fitting for Python, https://dx.doi.org/10.5281/zenodo.11813, https://lmfit.github.io/lmfit-py/intro.html (last access: August,2021)."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
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