{
 "cells": [
  {
   "cell_type": "markdown",
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   "source": [
    "# Horizontal wells"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A horizontal well is located in a 20 m thick aquifer; the hydraulic conductivity is $k = 10$ m/d and the vertical\n",
    "anisotropy factor is 0.1. The horizontal well is placed 5 m above the bottom of the\n",
    "aquifer. The well has a discharge of 1000 m$^3$/d and radius of $r=0.2$ m. The well\n",
    "is 200 m long and runs from $(x, y) = (−100, 0)$ to $(x, y) = (100, 0)$. \n",
    "\n",
    "Three-dimensional flow to the horizontal well is modeled by dividing the aquifer up in\n",
    "11 layers; the elevations are: `[20, 15, 10, 8, 6, 5.5, 5.2, 4.8, 4.4, 4, 2, 0]`. At\n",
    "the depth of the well, the layer thickness is equal to the diameter of the well, and it\n",
    "increases in the layers above and below the well. A transient timflow model is created with the\n",
    "Model3D command. The horizontal well is located in layer 6 and is modeled with the\n",
    "`DitchString` element."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "import timflow.transient as tft\n",
    "\n",
    "figsize = (6, 6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# parameters\n",
    "k = 10  # hydraulic conductivity, m/d\n",
    "Ss = 1e-4  # specific storage, 1/m\n",
    "anisotropy = 0.1  # kz / kh\n",
    "z = [20, 15, 10, 8, 6, 5.5, 5.2, 4.8, 4.4, 4, 2, 0]  # top and bottoms of layers, m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "ml = tft.Model3D(kaq=k, z=z, Saq=Ss, kzoverkh=anisotropy, tmin=0.1, tmax=100)\n",
    "nls = 21\n",
    "x = np.linspace(-100, 100, nls)\n",
    "y = np.zeros(nls)\n",
    "xy = np.vstack((x, y)).T\n",
    "hw = tft.DitchString(\n",
    "    ml, xy=xy, tsandQ=[(0, 1000)], layers=6\n",
    ")  # horizontal well in layer 6\n",
    "ml.solve()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "h = ml.headgrid(\n",
    "    np.linspace(-200, 200, 20),\n",
    "    np.linspace(-100, 100, 20),\n",
    "    t=[10, 20],\n",
    "    layers=range(7),\n",
    "    parallel=True,\n",
    "    show_progress=True,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "ml.plots.contour(win=[-200, 200, -100, 100], ngr=20, t=10, layers=6, parallel=True);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "hw.headinside(20)[0]  # returns heads in each line-sink (but they are all equal)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "t = np.linspace(1, 100, 100)\n",
    "hwinside = hw.headinside(t)\n",
    "plt.plot(t, hwinside[0, 0])\n",
    "plt.xlabel(\"time (d)\")\n",
    "plt.ylabel(\"head inside well (m)\")\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# contours in vertical cross-section. interpolation between cell centers\n",
    "ax = ml.plots.vcontour(\n",
    "    win=[-400, 400, 0, 0],\n",
    "    n=100,\n",
    "    t=50,\n",
    "    levels=20,\n",
    "    vinterp=True,\n",
    "    figsize=(16, 4),\n",
    "    horizontal_axis=\"x\",\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# contours in vertical cross-section. no interpolation between cell centers\n",
    "ax = ml.plots.vcontour(\n",
    "    win=[-400, 400, 0, 0],\n",
    "    n=100,\n",
    "    t=50,\n",
    "    levels=20,\n",
    "    vinterp=False,\n",
    "    figsize=(16, 4),\n",
    "    horizontal_axis=\"x\",\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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