{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Wells in different systems"
   ]
  },
  {
   "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",
    "plt.rcParams[\"font.size\"] = 8.0\n",
    "plt.rcParams[\"figure.figsize\"] = (8, 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "T = 500  # transmissivity\n",
    "S = 1e-4\n",
    "t = np.logspace(-2, 2, 101)\n",
    "r = 20\n",
    "Q = 1000"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Regular Theis well"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "ml = tft.ModelMaq(kaq=25, z=[20, 0], Saq=S / 20, tmin=0.01, tmax=100)\n",
    "w = tft.DischargeWell(ml, tsandQ=[(0, Q)], rw=1e-5)\n",
    "ml.solve()\n",
    "h1 = ml.head(r, 0, t)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Hantush for several different $c$ values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "clist = [1e2, 1e3, 1e4]\n",
    "hhantush = np.zeros((len(clist), len(t)))\n",
    "for i, c in enumerate(clist):\n",
    "    ml = tft.ModelMaq(\n",
    "        kaq=25, z=[21, 20, 0], c=c, Saq=S / 20, topboundary=\"semi\", tmin=0.01, tmax=100\n",
    "    )\n",
    "    w = tft.DischargeWell(ml, tsandQ=[(0, Q)], rw=1e-5)\n",
    "    ml.solve()\n",
    "    hhantush[i] = ml.head(r, 0, t)[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.semilogx(t, h1[0], label=\"Theis\")\n",
    "for i in range(3):\n",
    "    plt.semilogx(t, hhantush[i], label=\"c=\" + str(int(clist[i])))\n",
    "plt.legend(loc=\"best\")\n",
    "plt.title(\"head at r=20\")\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Two-aquifer system \n",
    "\n",
    "With same $T$ in both layers and several different $c$ values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "clist = [1e2, 1e3, 1e4]\n",
    "htwolayer = np.zeros((len(clist), len(t)))\n",
    "for i, c in enumerate(clist):\n",
    "    ml = tft.ModelMaq(\n",
    "        kaq=[25, 25],\n",
    "        z=[20, 0, -5, -25],\n",
    "        c=c,\n",
    "        Saq=S / 20,\n",
    "        topboundary=\"conf\",\n",
    "        tmin=0.01,\n",
    "        tmax=100,\n",
    "    )\n",
    "    w = tft.DischargeWell(ml, tsandQ=[(0, Q)], rw=1e-5)\n",
    "    ml.solve()\n",
    "    htwolayer[i] = ml.head(r, 0, t)[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.semilogx(t, h1[0], label=\"Theis\")\n",
    "for i in range(3):\n",
    "    plt.semilogx(t, htwolayer[i], label=\"c=\" + str(int(clist[i])))\n",
    "plt.legend(loc=\"best\")\n",
    "plt.title(\"head at r=20\")\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Model that starts at $t=10$ days"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "ml = tft.ModelMaq(kaq=25, z=[20, 0], Saq=S / 20, tmin=0.01, tmax=100, tstart=10)\n",
    "w = tft.DischargeWell(ml, tsandQ=[(10, Q)], rw=1e-5)\n",
    "ml.solve()\n",
    "ht10 = ml.head(r, 0, t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.semilogx(t, ht10[0], label=\"time shifted in model\")\n",
    "plt.semilogx(t + 10, h1[0], \"r--\", label=\"time shifted by hand\")\n",
    "plt.legend(loc=\"best\")\n",
    "plt.title(\"note that heads are not computed at the same times\")\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Well with entry resistance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "k = 25  # m/d\n",
    "H = 20  # m\n",
    "Ss = 1e-4 / H  # m^(-1)\n",
    "rw = 0.3  # m\n",
    "res = 0.1  # d\n",
    "Q = 500  # m^3/d\n",
    "ml = tft.Model3D(kaq=k, z=np.linspace(H, 0, 6), Saq=Ss, tmin=0.001, tmax=10)\n",
    "w = tft.Well(ml, tsandQ=[(0, Q)], rw=rw, res=res, layers=[0, 1, 2])\n",
    "ml.solve()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "hin = w.headinside(t=2)[:, 0]\n",
    "hout = ml.head(rw, 0, t=2, layers=[0, 1, 2])[:, 0]\n",
    "print(\"head inside well at t=2:     \", hin)\n",
    "print(\"head just outside well at t=2\", hout)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "print(\"discharge of screens at t=2\", w.discharge(2)[:, 0])\n",
    "Qcheck = 2 * np.pi * rw * ml.aq.Haq[:3] * (hout - hin) / res\n",
    "print(\"discharge from bc at t=2:  \", Qcheck)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Well with different entry resistance per layer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "k = 25  # m/d\n",
    "H = 20  # m\n",
    "Ss = 1e-4 / H  # m^(-1)\n",
    "rw = 0.3  # m\n",
    "res = [0.05, 0.1, 0.15]  # d\n",
    "Q = 500  # m^3/d\n",
    "ml = tft.Model3D(kaq=k, z=np.linspace(H, 0, 6), Saq=Ss, tmin=0.001, tmax=10)\n",
    "w = tft.Well(ml, tsandQ=[(0, Q)], rw=rw, res=res, layers=[0, 1, 2])\n",
    "ml.solve()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "hin = w.headinside(t=2)[:, 0]\n",
    "hout = ml.head(rw, 0, t=2, layers=[0, 1, 2])[:, 0]\n",
    "print(\"head inside well at t=2:     \", hin)\n",
    "print(\"head just outside well at t=2\", hout)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "print(\"discharge of screens at t=2\", w.discharge(2)[:, 0])\n",
    "Qcheck = 2 * np.pi * rw * ml.aq.Haq[:3] * (hout - hin) / res\n",
    "print(\"discharge from bc at t=2:  \", Qcheck)"
   ]
  }
 ],
 "metadata": {
  "language_info": {
   "name": "python"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}