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"cell_type": "markdown",
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"source": [
"# 2. Slug Test for Confined Aquifer - Multi-well"
]
},
{
"cell_type": "markdown",
"metadata": {
"editable": true,
"slideshow": {
"slide_type": ""
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"tags": []
},
"source": [
"### Import packages"
]
},
{
"cell_type": "code",
"execution_count": 1,
"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]"
]
},
{
"cell_type": "markdown",
"metadata": {
"editable": true,
"slideshow": {
"slide_type": ""
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"tags": []
},
"source": [
"## Introduction and Conceptual Model\n",
"\n",
"A well (Ln-2) fully penetrates a sandy confined aquifer of 6.1 m thickness. Additionally, a fully penetrating observation well (Ln-3) is located 6.45 m away from the test well. The slug displacement is 2.798 m. Head change was recorded at the slug well and the observation well. The well and casing radii of the slug well are 0.102 and 0.051 m, respectively. For the observation well, they are 0.071 and 0.025 m, respectively."
]
},
{
"cell_type": "markdown",
"metadata": {
"editable": true,
"slideshow": {
"slide_type": ""
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"tags": []
},
"source": [
"![](\"./figs/Multi_well.png\")
"
]
},
{
"cell_type": "markdown",
"metadata": {
"editable": true,
"slideshow": {
"slide_type": ""
},
"tags": []
},
"source": [
"### Load data"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"data1 = np.loadtxt(\"data/ln-2.txt\")\n",
"t1 = data1[:, 0] / 60 / 60 / 24 # convert time from seconds to days\n",
"h1 = data1[:, 1]\n",
"\n",
"data2 = np.loadtxt(\"data/ln-3.txt\")\n",
"t2 = data2[:, 0] / 60 / 60 / 24\n",
"h2 = data2[:, 1]"
]
},
{
"cell_type": "markdown",
"metadata": {
"editable": true,
"slideshow": {
"slide_type": ""
},
"tags": []
},
"source": [
"### Parameters and model"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"# known parameters\n",
"H0 = 2.798 # initial displacement, m\n",
"b = 6.1 # aquifer thickness, m\n",
"rw1 = 0.102 # well radius of Ln-2 Well, m\n",
"rw2 = 0.071 # well radius of observation Ln-3 Well, m\n",
"rc1 = 0.051 # casing radius of Ln-2 Well, m\n",
"r = 6.45 # distance from observation well to test well, m"
]
},
{
"cell_type": "markdown",
"metadata": {
"editable": true,
"slideshow": {
"slide_type": ""
},
"tags": []
},
"source": [
"Converting slug displacement into volume"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Slug: 0.02286 m^3\n"
]
}
],
"source": [
"Q = np.pi * rc1**2 * H0\n",
"print(f\"Slug: {Q:.5f} m^3\")"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"self.neq 1\n",
"solution complete\n"
]
}
],
"source": [
"ml = tft.ModelMaq(kaq=10, z=[0, -b], Saq=1e-4, tmin=1e-5, tmax=0.01)\n",
"w = tft.Well(ml, xw=0, yw=0, rw=rw1, rc=rc1, tsandQ=[(0, -Q)], layers=0, wbstype=\"slug\")\n",
"ml.solve()"
]
},
{
"cell_type": "markdown",
"metadata": {
"editable": true,
"slideshow": {
"slide_type": ""
},
"tags": []
},
"source": [
"### Estimate aquifer parameters\n",
"The hydraulic conductivity and specific storage are calibrated."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"...................................\n",
"Fit succeeded.\n"
]
}
],
"source": [
"# unknown parameters: kaq, Saq\n",
"cal = tft.Calibrate(ml)\n",
"cal.set_parameter(name=\"kaq\", layers=0, initial=10)\n",
"cal.set_parameter(name=\"Saq\", layers=0, initial=1e-4)\n",
"cal.seriesinwell(name=\"Ln-2\", element=w, t=t1, h=h1)\n",
"cal.series(name=\"Ln-3\", x=r, y=0, layer=0, t=t2, h=h2)\n",
"cal.fit()"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"
\n",
" \n",
" \n",
" | \n",
" optimal | \n",
"
\n",
" \n",
" \n",
" \n",
" | kaq_0_0 | \n",
" 1.166113 | \n",
"
\n",
" \n",
" | Saq_0_0 | \n",
" 0.000009 | \n",
"
\n",
" \n",
"
\n",
"
"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"hm1 = w.headinside(t1)\n",
"hm2 = ml.head(r, 0, t2, layers=0)\n",
"plt.semilogx(t1, h1 / H0, \".\", label=\"obs ln-2\")\n",
"plt.semilogx(t1, hm1[0] / H0, label=\"timflow ln-2\")\n",
"plt.semilogx(t2, h2 / H0, \".\", label=\"obs ln-3\")\n",
"plt.semilogx(t2, hm2[0] / H0, label=\"timflow ln-3\")\n",
"plt.xlabel(\"time [d]\")\n",
"plt.ylabel(\"Normalized Head: h/H0\")\n",
"plt.title(\"Model Results - Single layer model\")\n",
"plt.legend()\n",
"plt.grid()"
]
},
{
"cell_type": "markdown",
"metadata": {
"editable": true,
"slideshow": {
"slide_type": ""
},
"tags": []
},
"source": [
"### Comparison of results\n",
"\n",
"The values in `timflow` are compared with the KGS analytical model (Hyder et al. 1994) implemented in AQTESOLV (Duffield, 2007), and to the MLU model (Hemker & Post, 2014). The parameters of `timflow`and AQTESOLV are very similar. MLU differs a bit, this is likely due to the added skin resistance (skin factor of 2.42). "
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
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"\n",
"\n",
" \n",
" \n",
" | | \n",
" k [m/d] | \n",
" Ss [1/m] | \n",
" RMSE [m] | \n",
"
\n",
" \n",
" \n",
" \n",
" | timflow | \n",
" 1.17 | \n",
" 9.38e-06 | \n",
" 0.010 | \n",
"
\n",
" \n",
" | AQTESOLV | \n",
" 1.17 | \n",
" 9.37e-06 | \n",
" - | \n",
"
\n",
" \n",
" | MLU | \n",
" 1.31 | \n",
" 8.20e-06 | \n",
" - | \n",
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\n",
" \n",
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\n"
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""
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"source": [
"t = pd.DataFrame(\n",
" columns=[\"k [m/d]\", \"Ss [1/m]\", \"RMSE [m]\"],\n",
" index=[\"timflow\", \"AQTESOLV\", \"MLU\"],\n",
")\n",
"\n",
"t.loc[\"timflow\"] = np.append(cal.parameters[\"optimal\"].values, cal.rmse())\n",
"t.loc[\"AQTESOLV\"] = [1.166, 9.369e-06, \"-\"]\n",
"t.loc[\"MLU\"] = [1.311, 8.197e-06, \"-\"]\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",
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"t_formatted"
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{
"cell_type": "markdown",
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"tags": []
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"source": [
"### References\n",
"\n",
"* Butler Jr., J.J. (1998), The Design, Performance, and Analysis of Slug Tests, Lewis Publishers, Boca Raton, Florida, 252p.\n",
"* Hemker, K. and Post V. (2014) MLU for Windows: well flow modeling in multilayer aquifer systems; MLU User's guide. https://eur03.safelinks.protection.outlook.com/?url=https%3A%2F%2Fmicrofem.com%2Fdownload%2Fmlu-user.pdf&data=05%7C02%7CMark.Bakker%40tudelft.nl%7Cad7f16364d2d4fd55dbf08de73832eaa%7C096e524d692940308cd38ab42de0887b%7C0%7C0%7C639075204580287861%7CUnknown%7CTWFpbGZsb3d8eyJFbXB0eU1hcGkiOnRydWUsIlYiOiIwLjAuMDAwMCIsIlAiOiJXaW4zMiIsIkFOIjoiTWFpbCIsIldUIjoyfQ%3D%3D%7C0%7C%7C%7C&sdata=OBoe8seXZUfoat89Dfr4g6lF%2Bn1FdtXqtp%2F18BMXCn0%3D&reserved=0\n",
"* Duffield, G.M. (2007), AQTESOLV for Windows Version 4.5 User's Guide, HydroSOLVE, Inc., Reston, VA.\n",
"* Hyder, Z., Butler Jr, J.J., McElwee, C.D. and Liu, W. (1994), Slug tests in partially penetrating wells, Water Resources Research 30, 2945–2957."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
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