{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# A well in uniform flow"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Consider a well in the middle aquifer of a three aquifer system. Aquifer properties are given in Table 1. The well is located at $(x,y)=(0,0)$, the discharge is $Q=10,000$ m$^3$/d and the radius is 0.2 m. There is a uniform flow from West to East with a gradient of 0.002. The head is fixed to 20 m at a distance of 10,000 m downstream of the well. Here is the cookbook recipe to build this model:\n",
    "    \n",
    "* Import numpy: `import numpy as np`\n",
    "* Import pyplot for plotting: `import matplotlib.pyplot as plt`\n",
    "* import timflow.steady as tfs: `import timflow.steady as tfs`\n",
    "* Create the model and give it a name, for example `ml` with the command `ml = tml.ModelMaq(kaq, z, c)` (substitute the correct lists for `kaq`, `z`, and `c`).\n",
    "* Enter the well with the command `w = tml.Well(ml, xw, yw, Qw, rw, layers)`, where the well is called `w`.\n",
    "* Enter uniform flow with the command `tml.Uflow(ml, slope, angle)`.\n",
    "* Enter the reference head with `tml.Constant(ml, xr, yr, head, layer)`.\n",
    "* Solve the model `ml.solve()`\n",
    "\n",
    "**Table 1: Aquifer data for exercise 1**\n",
    "|Layer        |$k$ (m/d)|$z_b$ (m)|$z_t$|$c$ (days)|\n",
    "|-------------|--------:|--------:|----:|---------:|\n",
    "|Aquifer 0    |    10   |   -20   |  0  |    -     |\n",
    "|Leaky Layer 1|     -   |   -40   | -20 |  4000    |   \n",
    "|Aquifer 1    |    20   |   -80   | -40 |    -     |\n",
    "|Leaky Layer 2|     -   |   -90   | -80 |  10000   | \n",
    "|Aquifer 2    |     5   |   -140  | -90 |    -     ||\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "import timflow.steady as tfs\n",
    "\n",
    "figsize = (6, 6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "ml = tfs.ModelMaq(kaq=[10, 20, 5], z=[0, -20, -40, -80, -90, -140], c=[4000, 10000])\n",
    "w = tfs.Well(ml, xw=0, yw=0, Qw=10000, rw=0.2, layers=1)\n",
    "tfs.Constant(ml, xr=10000, yr=0, hr=20, layer=0)\n",
    "tfs.Uflow(ml, slope=0.002, angle=0)\n",
    "ml.solve()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Questions:\n",
    "### Exercise 1a\n",
    "What are the leakage factors of the aquifer system?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "print(\"The leakage factors of the aquifers are:\")\n",
    "print(ml.aq.lab)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise 1b\n",
    "What is the head at the well?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "print(\"The head at the well is:\")\n",
    "print(w.headinside())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise 1c\n",
    "Create a contour plot of the head in the three aquifers. Use a window with lower left hand corner $(x,y)=(−3000,−3000)$ and upper right hand corner $(x,y)=(3000,3000)$. Notice that the heads in the three aquifers are almost equal at three times the largest leakage factor."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "ml.plots.contour(\n",
    "    win=[-3000, 3000, -3000, 3000],\n",
    "    ngr=50,\n",
    "    layers=[0, 1, 2],\n",
    "    levels=10,\n",
    "    legend=True,\n",
    "    figsize=figsize,\n",
    ");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise 1d\n",
    "Create a contour plot of the head in aquifer 1 with labels along the contours. Labels are added when the `labels` keyword argument is set to `True`. The number of decimal places can be set with the `decimals` keyword argument, which is zero by default."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "ml.plots.contour(\n",
    "    win=[-3000, 3000, -3000, 3000],\n",
    "    ngr=50,\n",
    "    layers=[1],\n",
    "    levels=np.arange(30, 45, 1),\n",
    "    labels=True,\n",
    "    legend=[\"layer 1\"],\n",
    "    figsize=figsize,\n",
    ");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise 1e\n",
    "Create a contour plot with a vertical cross-section below it. Start three pathlines from $(x,y)=(-2000,-1000)$ at levels $z=-120$, $z=-60$, and $z=-10$. Try a few other starting locations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "win = [-3000, 3000, -3000, 3000]\n",
    "axes = ml.plots.topview_and_xsection(win=win, figsize=figsize)\n",
    "ml.plots.tracelines(\n",
    "    -2000 * np.ones(3),\n",
    "    -1000 * np.ones(3),\n",
    "    [-120, -60, -10],\n",
    "    hstepmax=50,\n",
    "    win=win,\n",
    "    orientation=\"both\",\n",
    "    ax=axes,\n",
    ")\n",
    "ml.plots.tracelines(\n",
    "    0 * np.ones(3),\n",
    "    1000 * np.ones(3),\n",
    "    [-120, -50, -10],\n",
    "    hstepmax=50,\n",
    "    win=win,\n",
    "    orientation=\"both\",\n",
    "    ax=axes,\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise 1f\n",
    "Add an abandoned well that is screened in both aquifer 0 and aquifer 1, located at $(x, y) = (100, 100)$ and create contour plot of all aquifers near the well (from (-200,-200) till (200,200)). What are the discharge and the head at the abandoned well? Note that you have to solve the model again!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "ml = tfs.ModelMaq(kaq=[10, 20, 5], z=[0, -20, -40, -80, -90, -140], c=[4000, 10000])\n",
    "w = tfs.Well(ml, xw=0, yw=0, Qw=10000, rw=0.2, layers=1)\n",
    "tfs.Constant(ml, xr=10000, yr=0, hr=20, layer=0)\n",
    "tfs.Uflow(ml, slope=0.002, angle=0)\n",
    "wabandoned = tfs.Well(ml, xw=100, yw=100, Qw=0, rw=0.2, layers=[0, 1])\n",
    "ml.solve()\n",
    "ml.plots.contour(\n",
    "    win=[-200, 200, -200, 200],\n",
    "    ngr=50,\n",
    "    layers=[0, 2],\n",
    "    levels=20,\n",
    "    color=[\"C0\", \"C1\", \"C2\"],\n",
    "    legend=True,\n",
    "    figsize=figsize,\n",
    ");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "print(\"The head at the abandoned well is:\")\n",
    "print(wabandoned.headinside())\n",
    "print(\"The discharge at the abandoned well is:\")\n",
    "print(wabandoned.discharge())"
   ]
  }
 ],
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   "name": "python"
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