termo.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Thermodynamics\n",
    "### Phase equilibrium\n",
    "##### UNIFAC method - Activity coefficient"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import CoolProp.CoolProp as CP\n",
    "import scipy.optimize as opt\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "#from UNIFAC import *\n",
    "plt.style.use('ggplot')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Molecular group data, extracted from the course material."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "      <th>8</th>\n",
       "      <th>9</th>\n",
       "      <th>10</th>\n",
       "      <th>11</th>\n",
       "      <th>12</th>\n",
       "      <th>13</th>\n",
       "      <th>14</th>\n",
       "      <th>15</th>\n",
       "      <th>16</th>\n",
       "      <th>17</th>\n",
       "      <th>18</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.00</td>\n",
       "      <td>8602.000</td>\n",
       "      <td>61.13</td>\n",
       "      <td>76.50</td>\n",
       "      <td>986.5</td>\n",
       "      <td>697.2</td>\n",
       "      <td>1318.0</td>\n",
       "      <td>1333.0</td>\n",
       "      <td>476.40</td>\n",
       "      <td>677.0</td>\n",
       "      <td>232.100</td>\n",
       "      <td>507.0</td>\n",
       "      <td>251.50</td>\n",
       "      <td>391.500</td>\n",
       "      <td>255.70</td>\n",
       "      <td>206.60</td>\n",
       "      <td>920.70</td>\n",
       "      <td>287.800</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-35.36</td>\n",
       "      <td>0.000</td>\n",
       "      <td>38.81</td>\n",
       "      <td>74.15</td>\n",
       "      <td>524.1</td>\n",
       "      <td>787.6</td>\n",
       "      <td>270.6</td>\n",
       "      <td>526.1</td>\n",
       "      <td>182.60</td>\n",
       "      <td>448.8</td>\n",
       "      <td>37.850</td>\n",
       "      <td>333.5</td>\n",
       "      <td>214.50</td>\n",
       "      <td>240.900</td>\n",
       "      <td>163.90</td>\n",
       "      <td>61.11</td>\n",
       "      <td>749.30</td>\n",
       "      <td>2811.500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-11.12</td>\n",
       "      <td>3.446</td>\n",
       "      <td>0.00</td>\n",
       "      <td>167.00</td>\n",
       "      <td>636.1</td>\n",
       "      <td>637.4</td>\n",
       "      <td>903.8</td>\n",
       "      <td>1329.0</td>\n",
       "      <td>25.77</td>\n",
       "      <td>347.3</td>\n",
       "      <td>5.994</td>\n",
       "      <td>287.1</td>\n",
       "      <td>32.14</td>\n",
       "      <td>161.700</td>\n",
       "      <td>122.80</td>\n",
       "      <td>9049.00</td>\n",
       "      <td>648.20</td>\n",
       "      <td>-4.449</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-69.70</td>\n",
       "      <td>-113.600</td>\n",
       "      <td>-146.80</td>\n",
       "      <td>0.00</td>\n",
       "      <td>803.2</td>\n",
       "      <td>603.3</td>\n",
       "      <td>5695.0</td>\n",
       "      <td>4.9</td>\n",
       "      <td>-52.10</td>\n",
       "      <td>586.8</td>\n",
       "      <td>5688.000</td>\n",
       "      <td>197.8</td>\n",
       "      <td>213.10</td>\n",
       "      <td>19.020</td>\n",
       "      <td>-49.29</td>\n",
       "      <td>23.50</td>\n",
       "      <td>663.20</td>\n",
       "      <td>52.800</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>156.40</td>\n",
       "      <td>457.000</td>\n",
       "      <td>89.60</td>\n",
       "      <td>25.82</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-137.1</td>\n",
       "      <td>353.5</td>\n",
       "      <td>-259.7</td>\n",
       "      <td>84.00</td>\n",
       "      <td>-203.6</td>\n",
       "      <td>101.100</td>\n",
       "      <td>267.8</td>\n",
       "      <td>28.06</td>\n",
       "      <td>8.642</td>\n",
       "      <td>42.70</td>\n",
       "      <td>-3210.00</td>\n",
       "      <td>-52.39</td>\n",
       "      <td>170.000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        1         2       3       4      5      6       7       8       9  \\\n",
       "1    0.00  8602.000   61.13   76.50  986.5  697.2  1318.0  1333.0  476.40   \n",
       "2  -35.36     0.000   38.81   74.15  524.1  787.6   270.6   526.1  182.60   \n",
       "3  -11.12     3.446    0.00  167.00  636.1  637.4   903.8  1329.0   25.77   \n",
       "4  -69.70  -113.600 -146.80    0.00  803.2  603.3  5695.0     4.9  -52.10   \n",
       "5  156.40   457.000   89.60   25.82    0.0 -137.1   353.5  -259.7   84.00   \n",
       "\n",
       "      10        11     12      13       14      15       16      17        18  \n",
       "1  677.0   232.100  507.0  251.50  391.500  255.70   206.60  920.70   287.800  \n",
       "2  448.8    37.850  333.5  214.50  240.900  163.90    61.11  749.30  2811.500  \n",
       "3  347.3     5.994  287.1   32.14  161.700  122.80  9049.00  648.20    -4.449  \n",
       "4  586.8  5688.000  197.8  213.10   19.020  -49.29    23.50  663.20    52.800  \n",
       "5 -203.6   101.100  267.8   28.06    8.642   42.70 -3210.00  -52.39   170.000  "
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "groups = { # main: {secondary i:[molecule,R,Q],secondary i+1:[molécula,R,Q],etc}\n",
    "    1: {1:['CH3',0.9011,0.848],2:['CH2',0.6744,0.540],3:['CH',0.4469,0.228],4:['C',0.2195,0]},\n",
    "    2: {5:['CH2CH',1.3454,1.176],6:['CHCH',1.1167,0.867],7:['CH2C',1.1173,0.988],8:['CHC',0.8886,0.676],70:['CC',0.6605,0.485]},\n",
    "    3: {9:['ACH',0.5313,0.400],10:['AC',0.3652,0.120]},\n",
    "    4: {11:['ACCH3',1.2663,0.968],12:['ACCH2',1.0396,0.660],13:['ACCH',0.8121,0.348]},\n",
    "    5: {14:['OH',1.000,1.200]},\n",
    "    6: {15:['CH3OH',1.4311,1.432]},\n",
    "    7: {16:['H2O',0.9200,1.400]},\n",
    "    8: {17:['ACOH',0.8952,0.680]},\n",
    "    9: {18:['CH3CO',1.6724,1.488],19:['CH2CO',1.4457,1.180]},\n",
    "    10: {20:['CHO',0.9980,0.948]},\n",
    "    11: {21:['CH3COO',1.9031,1.728],22:['CH2COO',1.6764,1.420]},\n",
    "    12: {23:['HCOO',1.2420,1.188]}\n",
    "}\n",
    "g_groups = {}\n",
    "for i in groups.values():\n",
    "    g_groups.update(i)\n",
    "\n",
    "global g_groups\n",
    "    \n",
    "a_mn = pd.read_csv('a-mn.csv', sep=';', index_col=0)\n",
    "a_mn.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## UNIFAC Method\n",
    "#### >> brief explanation goes here <<\n",
    "\n",
    "**Molecule class and it's methods:**\n",
    "* initializer - molecular group code and its respective amount\n",
    "\n",
    "\\> **combinatiorial activity coefficient** - _the easy one_\n",
    "* r, q and l coefficients\n",
    "* $\\phi$ and $\\theta$ factors\n",
    "* $\\gamma^c$- combinatorial activity coefficient\n",
    "\n",
    "\\> **residual activity coefficient** - _the tough one_\n",
    "* $\\psi$ factor\n",
    "* $\\Gamma_k$, X and $\\theta$\n",
    "* $\\Gamma_k^i$, $X^i$ and $\\theta^i$\n",
    "        \n",
    "$$\\ln{\\gamma^r} = \\sum \\nu_k (\\ln\\Gamma_k - \\ln\\Gamma_k^i)$$\n",
    "\n",
    "\\> **acitivity coefficient**\n",
    "\n",
    "$$\\ln{\\gamma} = \\ln{\\gamma^c} + \\ln{\\gamma^r}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class molecule():\n",
    "    def __init__(self,molGroups):\n",
    "        self.g = molGroups.keys()\n",
    "        self.v = molGroups.values()\n",
    "        self.groups = molGroups        \n",
    "        \n",
    "    def rql(self):\n",
    "        z,r,q = 10,0,0        \n",
    "        num = len(self.g)\n",
    "        if num > 1:\n",
    "            for i,k in zip(self.g,self.v):\n",
    "                r += g_groups[i][1] * k\n",
    "                q += g_groups[i][2] * k\n",
    "        else:\n",
    "            r = g_groups[tuple(self.g)[0]][1] * tuple(self.v)[0]\n",
    "            q = g_groups[tuple(self.g)[0]][2] * tuple(self.v)[0]\n",
    "        self.l = 0.5 * z * (r - q) - (r - 1)\n",
    "        self.r,self.q = r,q\n",
    "        return(self.r,self.q,self.l)\n",
    "    \n",
    "    def phi_theta(self, fluid):        \n",
    "        self.x, fluid.x = x, (1-x)\n",
    "        phi,theta = {},{}       \n",
    "        phi[self] = self.r * x / (self.r * self.x + fluid.r * fluid.x)\n",
    "        phi[fluid] = fluid.r * (1 - x) / (self.r * self.x + fluid.r * fluid.x)\n",
    "        theta[self] = self.q * x / (self.q * x + fluid.q * (1 - x))\n",
    "        theta[fluid] = fluid.q * (1 - x) / (self.q * self.x + fluid.q * fluid.x)\n",
    "        self.phi, self.theta = phi[self], theta[self]\n",
    "        fluid.phi, fluid.theta = phi[fluid], theta[fluid]\n",
    "        return(self.phi, self.theta, fluid.phi, fluid.theta)\n",
    "    \n",
    "    def combinatorial(self, fluid):\n",
    "        self.phi_theta(fluid)\n",
    "        self.x, fluid.x = x, (1-x)\n",
    "        self.gamma_c_ln = np.log(self.phi / self.x) + 5 * self.q * np.log(self.theta / self.phi) + \\\n",
    "                    self.l - (self.phi / self.x) * ( fluid.x * fluid.l + self.x * self.l )\n",
    "        fluid.gamma_c_ln = np.log(fluid.phi / fluid.x) + 5 * fluid.q * np.log(fluid.theta / fluid.phi) + \\\n",
    "                    fluid.l - (fluid.phi / fluid.x) * ( self.x * self.l + fluid.x * fluid.l )\n",
    "        self.gamma = np.exp(self.gamma_c_ln)\n",
    "        fluid.gamma = np.exp(fluid.gamma_c_ln)\n",
    "        return(self.gamma_c_ln, fluid.gamma_c_ln)    \n",
    "        \n",
    "    def psi_mod(self, fluid, pairs):\n",
    "        self.p = tuple([(i,j) for i in pairs for j in pairs])\n",
    "        a, psi = {}, {}\n",
    "        for i in self.p:\n",
    "            j = (i[0]-1,i[1]-1)\n",
    "            a[i] = a_mn.iat[j]\n",
    "            psi[i] = np.exp(-a_mn.iat[j] / T)\n",
    "        self.a_k, self.a_v, self.a = a.keys(), a.values(), a\n",
    "        self.psi_k, self.psi_v, self.psi = psi.keys(), psi.values(), psi\n",
    "        self.psi_matrix = np.reshape(np.array([self.psi[i] for i in self.p]),(len(pairs),len(pairs)))\n",
    "        return(self.a_k, self.a_v, self.a)\n",
    "        return(self.psi_k, self.psi_v, self.psi)\n",
    "        return(self.p)\n",
    "        return(self.psi_matrix)\n",
    "    \n",
    "    def X_mod(self, fluid):            \n",
    "        self.x, fluid.x = x, (1-x)\n",
    "        den = sum([self.groups[k] for k in list(self.g)]) * self.x + \\\n",
    "              sum([fluid.groups[k] for k in list(fluid.g)]) * fluid.x\n",
    "        X = []\n",
    "        g_list = list(set([i for j in [list(self.g),list(fluid.g)] for i in j]))\n",
    "        for k in sorted(g_list):\n",
    "            nom = 0\n",
    "            if k in list(self.g):\n",
    "                nom += self.groups[k] * self.x\n",
    "            if k in list(fluid.g):\n",
    "                nom += fluid.groups[k] * fluid.x\n",
    "            X.append(nom / den)      \n",
    "        self.X = X       \n",
    "        return(self.X)\n",
    "    \n",
    "    def X_mod_i(self, fluid):   \n",
    "        v1, v2 = list(self.v), list(fluid.v)\n",
    "        Xi = np.array(v1) / sum(v1), np.array(v2) / sum(v2)\n",
    "        self.Xi = Xi\n",
    "        return(self.Xi)\n",
    "    \n",
    "    def Theta_mod(self, fluid):\n",
    "        Xx = self.X_mod(fluid)\n",
    "        g_list = list(set([i for j in [list(self.g),list(fluid.g)] for i in j]))\n",
    "        nom = np.multiply(np.transpose(Xx) ,np.array([g_groups[k][2] for k in sorted(g_list)]))\n",
    "        den = sum(nom)\n",
    "        self.Theta = np.divide(nom, den)\n",
    "        return(self.Theta)\n",
    "    \n",
    "    def Theta_mod_i(self, fluid):\n",
    "        X_i = self.X_mod_i(fluid)\n",
    "        g1, g2 = list(self.g), list(fluid.g)\n",
    "        Q1, Q2 = [g_groups[i][2] for i in g1], [g_groups[i][2] for i in g2]\n",
    "        #print(X_i,'\\n',Q1,'\\n',Q2)\n",
    "        nom1, nom2 = np.multiply(X_i[0],Q1), np.multiply(X_i[1],Q2)\n",
    "        den1, den2 = sum(nom1), sum(nom2)\n",
    "        self.Theta1, self.Theta2 = nom1 / den1, nom2 / den2\n",
    "        return(self.Theta1, self.Theta2)\n",
    "    \n",
    "    def Gamma_k(self, fluid):        \n",
    "        t = self.Theta_mod(fluid)\n",
    "        g_list = list(set([i for j in [list(self.g),list(fluid.g)] for i in j]))\n",
    "        Q = [g_groups[k][2] for k in sorted(g_list)]\n",
    "        YY = self.psi_matrix\n",
    "        nTheta = np.reshape(t,(len(YY),1))\n",
    "        pt = np.multiply(YY,nTheta)\n",
    "        pt2 = np.multiply(YY,t)\n",
    "        denom = np.sum(pt,axis=0)\n",
    "        gam = 1 - np.log(denom) - np.sum(np.divide([i for i in pt2],denom),axis=1)\n",
    "        self.gamma_k_ln = np.multiply(Q,gam)\n",
    "        return(self.gamma_k_ln)\n",
    "    \n",
    "    def Gamma_k_i(self, fluid):\n",
    "        t1, t2 = self.Theta_mod_i(fluid)    \n",
    "        g1, g2 = list(self.g), list(fluid.g)\n",
    "        Q1, Q2 = [g_groups[i][2] for i in g1], [g_groups[i][2] for i in g2]\n",
    "        YY = self.psi_matrix\n",
    "        if len(YY) == 3:\n",
    "            a, b = np.multiply([YY[0,0],YY[2,0]], t1), np.multiply([YY[0,2],YY[2,2]], t1)\n",
    "            c, d = np.multiply([YY[0,0],YY[1,0]], t2), np.multiply([YY[0,1],YY[1,1]], t2)\n",
    "            e, f = np.multiply([YY[0,0],YY[0,2]], t1), np.multiply([YY[2,0],YY[2,2]], t1)\n",
    "            g, h = np.multiply([YY[0,0],YY[0,1]], t1), np.multiply([YY[1,0],YY[1,1]], t2)\n",
    "            gamma_1 = Q1[0] * (1 - np.log(sum(a)) - e[0] / sum(a) - e[1] / sum(b) )\n",
    "            gamma_2 = Q1[1] * (1 - np.log(sum(b)) - f[0] / sum(a) - f[1] / sum(b) )\n",
    "            gamma_3 = Q2[0] * (1 - np.log(sum(c)) - g[0] / sum(c) - g[1] / sum(d) )\n",
    "            gamma_4 = Q2[1] * (1 - np.log(sum(d)) - h[0] / sum(c) - h[1] / sum(d) ) \n",
    "        else:\n",
    "            a, b = np.multiply([YY[0,0],YY[1,0]], t1), np.multiply([YY[0,1],YY[1,1]], t1)\n",
    "            c, d = np.multiply([YY[0,0],YY[1,0]], t2), np.multiply([YY[0,1],YY[1,1]], t2)\n",
    "            e, f = np.multiply([YY[0,0],YY[0,1]], t1), np.multiply([YY[1,0],YY[1,1]], t1)\n",
    "            g, h = np.multiply([YY[0,0],YY[0,1]], t1), np.multiply([YY[1,0],YY[1,1]], t2)\n",
    "            gamma_1 = Q1[0] * (1 - np.log(sum(a)) - e[0] / sum(a) - e[1] / sum(b) )\n",
    "            gamma_2 = Q1[1] * (1 - np.log(sum(b)) - f[0] / sum(a) - f[1] / sum(b) )\n",
    "            gamma_3 = Q2[0] * (1 - np.log(sum(c)) - g[0] / sum(c) - g[1] / sum(d) )\n",
    "            gamma_4 = Q2[1] * (1 - np.log(sum(d)) - h[0] / sum(c) - h[1] / sum(d) )\n",
    "        return(gamma_1,gamma_2,gamma_3,gamma_4)\n",
    "    \n",
    "    def residual(self, fluid):\n",
    "        v1, v2 = list(self.v), list(fluid.v)\n",
    "        k_i = self.Gamma_k_i(fluid)\n",
    "        g2 = np.array([self.Gamma_k(fluid)[0],self.Gamma_k(fluid)[1]])\n",
    "        if len(self.Gamma_k(fluid)) == 3:\n",
    "            g1 = np.array([self.Gamma_k(fluid)[0],self.Gamma_k(fluid)[2]])\n",
    "        else:\n",
    "            g1 = g2        \n",
    "        gg1 = g1-k_i[:2]\n",
    "        gg2 = g2-k_i[2:]\n",
    "        gamma_r_ln_1 = sum(np.multiply(v1,gg1))\n",
    "        gamma_r_ln_2 = sum(np.multiply(v2,gg2))\n",
    "        gamma_r_1, gamma_r_2 = np.exp(gamma_r_ln_1), np.exp(gamma_r_ln_2)\n",
    "        return(gamma_r_ln_1, gamma_r_ln_2)\n",
    "    \n",
    "    def Gamma(self, fluid):\n",
    "        yr = self.residual(fluid)\n",
    "        yc = self.combinatorial(fluid)\n",
    "        y_ln = np.add(yr, yc)\n",
    "        self.y = np.exp(y_ln)\n",
    "        return(self.y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Peng-Robinson Equation**\n",
    "\n",
    "\\begin{equation}\n",
    "p = \\frac{RT}{v-b} - \\frac{a}{v^2+2bv-b^2}\n",
    "\\end{equation}\n",
    "\n",
    "where:\n",
    "\\begin{equation}\n",
    "a_i = \\frac{0.45724 R^2 T_c^2}{p_c} \\times \\left[1 + (0.37464 + 1.54226 \\omega - 0.26992 \\omega^2)(1-\\sqrt{\\frac{T}{T_c}})\\right]^2\n",
    "\\end{equation}\n",
    "\n",
    "or\n",
    "\\begin{equation}\n",
    "a_i = \\frac{0.45724 R^2 T_c^2}{p_c} \\times \\alpha(T)\n",
    "\\end{equation}\n",
    "\n",
    "with\n",
    "\n",
    "\\begin{equation}\n",
    "\\alpha\\left(T\\right) = \\left[1 + (0.37464 + 1.54226 \\omega - 0.26992 \\omega^2)(1-\\sqrt{\\frac{T}{T_c}})\\right]^2\n",
    "\\end{equation}\n",
    "\n",
    "\\begin{equation}\n",
    "b_i = \\frac{0.07780 R T_c}{p_c}\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Isobutane** - pure\n",
    "* Properties: $p_{sat}$,$T_c$, $p_c$, $\\omega$\n",
    "* Constants: a, b, $\\alpha(T)$\n",
    "\n",
    "**Propane** - pure\n",
    "* Properties: $p_{sat}$,$T_c$, $p_c$, $\\omega$\n",
    "* Constants: a, b, $\\alpha(T)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "R = 8.314\n",
    "T = 303.14\n",
    "\n",
    "## Propane\n",
    "p_sat_prop = CP.PropsSI('P','T',T,'Q',0,'Propane') / 1000\n",
    "p_crit_prop = CP.PropsSI('pcrit','Propane') / 1000\n",
    "T_crit_prop = CP.PropsSI('Tcrit','Propane')\n",
    "w_prop = CP.PropsSI('acentric','T',T,'Q',0,'Propane')\n",
    "##\n",
    "alpha_prop = 1 + (0.37464 + 1.54226 * w_prop - 0.26992 * w_prop**2) * (1 - np.sqrt(T / T_crit_prop))\n",
    "a_prop = 0.45724 *( (R * T_crit_prop) ** 2 / p_crit_prop) * alpha_prop**2 / 1000\n",
    "b_prop = 0.07780 * R * T_crit_prop / p_crit_prop / 1000\n",
    "\n",
    "## Butane\n",
    "kPatommHg = 760 / 101.325\n",
    "p_sat_but = CP.PropsSI('P','T',T,'Q',0,'nButane') / 1000\n",
    "p_crit_but = CP.PropsSI('pcrit','nButane') / 1000\n",
    "T_crit_but = CP.PropsSI('Tcrit','nButane')\n",
    "w_but = CP.PropsSI('acentric','T',T,'Q',0,'nButane')\n",
    "##\n",
    "alpha_but = 1 + (0.37464 + 1.54226 * w_but - 0.26992 * w_but**2) * (1 - np.sqrt(T / T_crit_but))\n",
    "a_but = 0.45724 *( (R * T_crit_but) ** 2 / p_crit_but) * alpha_but**2 / 1000\n",
    "b_but = 0.07780 * R * T_crit_but / p_crit_but / 1000"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Mixture**\n",
    "\n",
    "\\begin{equation}\n",
    "a = \\sum\\limits_j \\sum\\limits_i x_i x_j \\sqrt{(a_i a_j)}\n",
    "\\end{equation}\n",
    "\n",
    "\\begin{equation}\n",
    "b = \\sum\\limits_i x_i b_i\n",
    "\\end{equation}\n",
    "\n",
    "i.e\n",
    "\n",
    "\\begin{equation}\n",
    "p = \\frac{\\left(N_1 + N_2 \\right)RT}{V-N_1 b_1 - N_2 b_2} - \\frac{N_1^2 a_1 + N_1 N_2 \\sqrt{a_1 a_2} + N_2^2 a_2}{V^2+2 \\left(N_1 b_1 + N_2 b_2 \\right)V-\\left(N_1 b_1 + N_2 b_2 \\right)^2}\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Peng-Robinson Equation of State - Compressibility Factor form\n",
    "\n",
    "$$A = \\frac{a P}{R^2 T^2}$$\n",
    "\n",
    "$$B = \\frac{b P}{ R T}$$\n",
    "\n",
    "$$Z = \\frac{1}{1  - B/Z} - \\frac{A}{B}\\frac{B/Z}{\\left[1 + 2 B/Z - \\left(B/Z\\right)^2\\right]}$$\n",
    "\n",
    "#### Fugacity Coefficient calculation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def phis(v):\n",
    "    yy, pp = v[0], v[1]\n",
    "    A_mult = pp / (R**2 * T**2)\n",
    "    B_mult = pp / (R * T)\n",
    "    A = A_mult * (yy**2 * a_prop + (1 - yy)**2 * a_but + yy * (1 - yy) * np.sqrt(a_but * a_prop))\n",
    "    B = B_mult * (yy * b_prop + (1 - yy) * b_but)\n",
    "    def Z_factor(comp):\n",
    "        Z = comp\n",
    "        return(1 / (1 - B / Z) - \\\n",
    "           (A / B) * (B / Z) / (1 + 2 * B / Z + (B / Z)**2) - Z)\n",
    "    \n",
    "    Z_f = opt.fsolve(Z_factor,1)    \n",
    "    phi_prop_v = np.exp((B_mult * b_prop / B) * (Z_f - 1) - np.log(Z_f - B) - \\\n",
    "                (A / (B * np.sqrt(8))) * np.log( (Z_f + B + B*np.sqrt(2)) /(Z_f + B - B*np.sqrt(2))) *\\\n",
    "        (2 *A_mult *(yy * a_prop + (1-yy) * a_but)/A - (B_mult * b_prop) / B))        \n",
    "    phi_but_v = np.exp((B_mult * b_but / B) * (Z_f - 1) - np.log(Z_f - B) - \\\n",
    "                (A / (B * np.sqrt(8))) * np.log( (Z_f + B + B*np.sqrt(2)) /(Z_f + B - B*np.sqrt(2))) *\\\n",
    "        (2 *A_mult *(yy * a_prop + (1-yy) * a_but)/A - (B_mult * b_but) / B))\n",
    "    return(phi_prop_v,phi_but_v)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def sistema(v):\n",
    "    yy, pp = v[0], v[1]\n",
    "    if ideal == 0:\n",
    "        phi_prop_v,phi_but_v = phis(v)\n",
    "        return(yy * pp * phi_prop_v[0]  - f_l_1,\n",
    "          (1-yy) * pp * phi_but_v[0] - f_l_2)\n",
    "    else:\n",
    "        return(yy * pp - f_l_1,\n",
    "          (1-yy) * pp - f_l_2)\n",
    "    \n",
    "\n",
    "T = 303.14\n",
    "act = []\n",
    "xx_molar = np.linspace(0.05,0.95,40)\n",
    "for x in xx_molar:\n",
    "    propane, isobutane = molecule({1:2,2:1}), molecule({1:2,2:2})\n",
    "    propane.rql(), isobutane.rql()    \n",
    "    propane.phi_theta(isobutane)\n",
    "    propane.combinatorial(isobutane)\n",
    "    propane.psi_mod(isobutane,[1,1])\n",
    "    propane.X_mod(isobutane)\n",
    "    propane.X_mod_i(isobutane)\n",
    "    propane.Theta_mod(isobutane)\n",
    "    propane.Gamma_k(isobutane)\n",
    "    propane.Theta_mod_i(isobutane)\n",
    "    propane.Gamma_k_i(isobutane)\n",
    "    propane.residual(isobutane)\n",
    "    propane.Gamma(isobutane)\n",
    "    act.append(propane.y)   \n",
    "\n",
    "\n",
    "guess = (0, p_sat_prop)    \n",
    "ideal = 1\n",
    "y1,p1 = [], []\n",
    "for i,x in enumerate(xx_molar):\n",
    "    f_l_1 = x * act[i][0] * p_sat_prop\n",
    "    f_l_2 = (1-x) * act[i][1] * p_sat_but\n",
    "    y, p =  opt.fsolve(sistema, guess)\n",
    "    guess = (y, p)\n",
    "    y1.append(y)\n",
    "    p1.append(p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## \\#Datamunging\n",
    "\n",
    "Cleaning and converting the data for a more suitable format"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Bubble point\n",
    "pb1, xb1 = [], []\n",
    "pb1.append([p_sat_but]), xb1.append([0])\n",
    "pb1.append([p for p in p1]), xb1.append(xx_molar)\n",
    "pb1.append([p_sat_prop]), xb1.append([1])\n",
    "pb1 = np.array(list([i for j in pb1 for i in j]))* kPatommHg\n",
    "xb1 = np.array(list([i for j in xb1 for i in j]))\n",
    "\n",
    "# Dew point\n",
    "pdew1, xd1 = [], []\n",
    "pdew1.append([p_sat_but]), xd1.append([0])\n",
    "pdew1.append([p for p in p1]), xd1.append(y1)\n",
    "pdew1.append([p_sat_prop]), xd1.append([1])\n",
    "pdew1 = np.array(list([i for j in pdew1 for i in j]))* kPatommHg\n",
    "xd1 = np.array(list([i for j in xd1 for i in j]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## \\#Dataviz\n",
    "\n",
    "Plotting charts for better understanding - visual grammar"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0xb33dc50>"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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VxZw5c3B3d+f69esaZ1A9evRg3LhxhIaG4urqip+fX5mPkkiSRMeOHfH29mbw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/F+T09P6HT8jofI1igUCowZ448xY/xx5owW69efwogR2/D44wMwa1Z/BAS4o6CgACdOnLD2UDuk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\nIomwZImIiCTy/4xm7v0YVEpEAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xb2fc7b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig1 = plt.figure(figsize=(7,8))\n",
    "fig1.text(0.27, 0.38, \"V\", fontsize=20, color=\"k\")\n",
    "fig1.text(0.39, 0.48, \"V + L\", fontsize=20, color=\"k\")\n",
    "fig1.text(0.59, 0.58, \"L\", fontsize=20, color=\"k\")\n",
    "ax1 = fig1.add_subplot(1,1,1)\n",
    "ax1.plot(1-xb1,pb1,color='blue',label=r\"Ponto de bolha - UNIFAC\")\n",
    "#ax.scatter((1-xb),pb)\n",
    "ax1.plot(1-xd1,pdew1,color='navy',label=r\"Ponto de orvalho - UNIFAC\")\n",
    "#ax.scatter(1-xd,pd)\n",
    "ax1.set_xlim([0,1])\n",
    "#ax.set_ylim([0,10000])\n",
    "ax1.set_xlabel(r'$x_1$ [-]', fontsize=18)\n",
    "ax1.set_ylabel(r'$P$  [mmHg]', fontsize=18)\n",
    "\n",
    "## dados experimentais\n",
    "x_beranek = np.array([0.096, 0.164, 0.257, 0.437, 0.867, 0.910])\n",
    "y_beranek = np.array([0.261, 0.388, 0.530, 0.707, 0.942, 0.958])\n",
    "p_beranek = np.array([354, 400.5, 468.1, 591, 947.4, 993.5]) * kPatommHg\n",
    "p_err = np.array([1.56,1.58,1.69,0,0.14,0.56]) * p_beranek / 100\n",
    "#x_beranek = np.array([0.065, 0.133, 0.216, 0.411, 0.535, 0.691, 0.854, 0.903])\n",
    "#y_beranek = np.array([0.144, 0.267, 0.400, 0.601, 0.710, 0.833, 0.918, 0.944])\n",
    "#p_beranek = np.array([906.3, 1003.5, 1127.5, 1413.1, 1638.8, 1938.9, 2236.1, 2357.3]) * kPatommHg\n",
    "\n",
    "\n",
    "ax1.scatter(1-x_beranek,p_beranek,color='blue',marker='s',s=20,\\\n",
    "            label=\"Ponto de bolha - \\nBeránek and Wichterle, 1980\")\n",
    "ax1.scatter(1-y_beranek,p_beranek,color='black',marker='s',s=20,\\\n",
    "            label=\"Ponto de orvalho -\\n Beránek and Wichterle, 1980\")\n",
    "ax1.legend(loc=1)\n",
    "ax1.set_title('Propano n-Butano (GLP)',fontsize=22)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### Pressure vessel project\n",
    "\n",
    "$$ \\sigma_1 = -p$$\n",
    "\n",
    "$$ \\sigma_2 = \\frac{p r}{t}$$\n",
    "\n",
    "$$ \\sigma_3 = \\frac{p r}{2t}$$\n",
    "\n",
    "where $t$ is the vessel wall thickness, $r$ its radius, $p$ the internal pressure and $\\sigma$ the tension state.\n",
    "\n",
    "#### von Mises criteria\n",
    "\n",
    "$$\\sigma_{adm} = \\sqrt{\\frac{1}{2}\\left[\\left(\\sigma_1 - \\sigma_2\\right)^2 + \\left(\\sigma_2 - \\sigma_3\\right)^2 + \\left(\\sigma_3 - \\sigma_1\\right)^2\\right]}$$\n",
    "\n",
    "We can, by selecting the material, and some standardized diameter, find the wall thickness given the mixture representative of GPL.\n",
    "\n",
    "$$\\sigma_{adm} = \\frac{2}{3}\\sigma_{yield}$$\n",
    "\n",
    "https://www.scribd.com/doc/30905197/Abnt-Nbr-8473-Regulador-de-Baixa-Pressao-para-Gas-Liquefeito-de-Petroleo-glp\n",
    "\n",
    "http://www.matweb.com/search/datasheet.aspx?MatGUID=b58ee61a3745453a9232f7864abba74f"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 1.46753658]\n",
      "[ 1.73049076]\n",
      "[ 1.99645892]\n",
      "[ 2.26523626]\n",
      "[ 2.53657708]\n",
      "[ 2.81018907]\n",
      "[ 3.08572679]\n",
      "[ 3.36278421]\n",
      "[ 3.64088639]\n",
      "[ 3.91947992]\n",
      "[ 1.2077654]\n"
     ]
    }
   ],
   "source": [
    "aaa = []\n",
    "for i,x_v in enumerate(np.linspace(0.1,0.9,9)):\n",
    "    T_v = 70 + 273.15\n",
    "    p_sat_prop_v = CP.PropsSI('P','T',T_v,'Q',0,'Propane') / 1000\n",
    "    p_sat_but_v = CP.PropsSI('P','T',T_v,'Q',0,'nButane') / 1000\n",
    "    x = x_v\n",
    "    new_veccv = []\n",
    "    propane, isobutane = molecule({1:2,2:1}), molecule({1:2,2:2})\n",
    "    propane.rql(), isobutane.rql()    \n",
    "    propane.phi_theta(isobutane)\n",
    "    propane.combinatorial(isobutane)\n",
    "    propane.psi_mod(isobutane,[1,1])\n",
    "    propane.X_mod(isobutane)\n",
    "    propane.X_mod_i(isobutane)\n",
    "    propane.Theta_mod(isobutane)\n",
    "    propane.Gamma_k(isobutane)\n",
    "    propane.Theta_mod_i(isobutane)\n",
    "    propane.Gamma_k_i(isobutane)\n",
    "    propane.residual(isobutane)\n",
    "    propane.Gamma(isobutane)\n",
    "    new_veccv.append(propane.y)\n",
    "    guess = (0, p_sat_prop_v)    \n",
    "    yv,pv = [], []\n",
    "    f_l_1 = x * new_veccv[0][0] * p_sat_prop_v\n",
    "    f_l_2 = (1-x) * new_veccv[0][1] * p_sat_but_v\n",
    "    y, p =  opt.fsolve(sistema, guess)\n",
    "    yv.append(y)\n",
    "    pv = p\n",
    "    D = 360          # diameter mm\n",
    "    sigma = 205000   # limite de escoamento aço 1020 kPa\n",
    "    sigma_adm = sigma * 2/3 # tensão máxima admissível\n",
    "    def espessura(chute):\n",
    "        tt = chute\n",
    "        sigma_1 = 1.3 * pv * (D/2) / tt\n",
    "        sigma_2 = sigma_1 / 2\n",
    "        sigma_3 = -1.3 * pv\n",
    "        return((sigma_1 - sigma_2)**2 + (sigma_2 - sigma_3)**2 + (sigma_3 - sigma_1)**2 - 2 *(sigma_adm)**2)\n",
    "    t_ = opt.fsolve(espessura, 0.1)\n",
    "    aaa.append(t_)\n",
    "    print(t_)\n",
    "pv = p_sat_prop_v\n",
    "print(opt.fsolve(espessura,0.1))\n",
    "pv = p_sat_but_v\n",
    "print(opt.fsolve(espessura,0.1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 1)"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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RUUCRxJ1cbG9Fzp8/7+sSAhqH7uTBPnsfe+x97LF3OZ0SCgvDMHRo80bE+eQ+IiIiP1JY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\nIP8PqcakUXp0cKMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xd0d4b00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figg = plt.figure(figsize=(8,4))\n",
    "ppl = figg.add_subplot(1,1,1)\n",
    "ppl.scatter(np.linspace(0,1,11),[1.2077654,1.46753658,1.73049076,1.99645892,2.26523626,2.53655708,2.81018907,3.08572679,\n",
    "                                 3.36278421,3.64088639,3.91947992])\n",
    "ppl.set_ylabel('t (mm)')\n",
    "ppl.set_xlabel('Composição (-)')\n",
    "ppl.set_title('Espessura de parede')\n",
    "ppl.set_xlim([0,1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Acetone n-Hexane mixture"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "T = 318.15\n",
    "ideal = 1\n",
    "new_vec = []\n",
    "x_molar = np.linspace(0.05,0.95,40)\n",
    "for x in x_molar:\n",
    "    hexano = molecule({1:2,2:3})\n",
    "    hexano = molecule({1:1,18:1})\n",
    "    hexano.rql(),acetona.rql()\n",
    "    acetona.rql()\n",
    "    acetona.phi_theta(hexano)\n",
    "    acetona.combinatorial(hexano)\n",
    "    acetona.psi_mod(hexano,[1,1,9])\n",
    "    acetona.X_mod(hexano)\n",
    "    acetona.X_mod_i(hexano)\n",
    "    acetona.Theta_mod(hexano)\n",
    "    acetona.Gamma_k(hexano)\n",
    "    acetona.Theta_mod_i(hexano)\n",
    "    acetona.Gamma_k_i(hexano)\n",
    "    acetona.residual(hexano)\n",
    "    acetona.Gamma(hexano)\n",
    "    new_vec.append(acetona.y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Source\n",
    "Rall W.: Dampfdruckuntersuchungen und Aktivitätskoeffizienten des Systems Aceton-n-Hexan. Z.Elektrochem. 62 (1958) 1090-1092\n",
    "http://www.ddbst.com/en/EED/VLE/VLE%20Acetone%3BHexane.php"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "45.06597516202516 68.32509345651765\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0xb8afcf8>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Z6Ns3B+bmmn2LvXqVhXnzInH/fgrWrGkPT087jZ6/JGX9csvJkWHMmF9gbm6A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bi5udGnTx88PDwYM2YM//jHP4CHRc/GxoYf/vCHAEyePFmdhhw3bhyTJk3iq6++ajO3MTExODs7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\nEEb6P3M9bCkRa+/FAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xb874a90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p_sat_pent = CP.PropsSI('P','T',T,'Q',0,'nHexane') / 1000\n",
    "p_sat_ace = CP.PropsSI('P','T',T,'Q',0,'Acetone') / 1000\n",
    "print(p_sat_pent,p_sat_ace)\n",
    "guess = (0, 0)    \n",
    "yk,pk = [], []\n",
    "#x_molar = np.linspace(0.1,0.9,100)\n",
    "for i,x in enumerate(x_molar):\n",
    "    f_l_1 = x * new_vec[i][0] * p_sat_ace\n",
    "    f_l_2 = (1-x) * new_vec[i][1] * p_sat_pent\n",
    "    y, p =  opt.fsolve(sistema, guess)\n",
    "    guess = (y, p)\n",
    "    yk.append(y)\n",
    "    pk.append(p)\n",
    "    \n",
    "# Bubble point\n",
    "pb, xb = [], []\n",
    "pb.append([p_sat_pent]), xb.append([0])\n",
    "pb.append([p for p in pk]), xb.append(x_molar)\n",
    "pb.append([p_sat_ace]), xb.append([1])\n",
    "pb = np.array(list([i for j in pb for i in j]))* kPatommHg\n",
    "xb = np.array(list([i for j in xb for i in j]))\n",
    "\n",
    "# Dew point\n",
    "pdew, xd = [], []\n",
    "pdew.append([p_sat_pent]), xd.append([0])\n",
    "pdew.append([p for p in pk]), xd.append(yk)\n",
    "pdew.append([p_sat_ace]), xd.append([1])\n",
    "pdew = np.array(list([i for j in pdew for i in j]))* kPatommHg\n",
    "xd = np.array(list([i for j in xd for i in j]))\n",
    "\n",
    "fig = plt.figure(figsize=(7,8))\n",
    "fig.text(0.46, 0.52, \"V\", fontsize=20, color=\"k\")\n",
    "fig.text(0.56, 0.62, \"V + L\", fontsize=20, color=\"k\")\n",
    "fig.text(0.76, 0.72, \"L\", fontsize=20, color=\"k\")\n",
    "ax = fig.add_subplot(1,1,1)\n",
    "ax.plot(1-xb,pb,color='blue',label=r\"Ponto de bolha - UNIFAC\")\n",
    "#ax.scatter((1-xb),pb)\n",
    "ax.plot(1-xd,pdew,color='navy',label=r\"Ponto de orvalho - UNIFAC\")\n",
    "#ax.scatter(1-xd,pd)\n",
    "ax.set_xlim([0,1])\n",
    "#ax.set_ylim([0,800])\n",
    "#matplotlib.rcParams.update({'font.size': 18, 'text.usetex': True})\n",
    "ax.set_xlabel(r'$x_1$ [-]', fontsize=18)\n",
    "ax.set_ylabel(r'$P$  [mmHg]', fontsize=18)\n",
    "\n",
    "x_ref = np.array([0,0.0651,0.1592,0.2549,0.3478,0.4429,0.521,0.5907,\n",
    "                  0.6202,0.7168,0.7932,0.8022,0.8692,0.9288,0.9658,1])\n",
    "y_ref= np.array([0,0.2828,0.4442,0.5163,0.556,0.5866,0.6068,0.6258,\n",
    "                 0.6339,0.6662,0.7034,0.7292,0.7583,0.8255,0.9003,1])\n",
    "p_ref = np.array([42.25,59.275,72.767,78.687,82.3,84.34,85.273,84.5,\n",
    "                 84.94,84.126,83.7,83.1,80.447,77.754,72.434,67.328]) * kPatommHg\n",
    "\n",
    "#x_ref = np.array([0,0.084,0.18,0.315,0.422,0.532,0.649,0.785,0.916,1])\n",
    "#y_ref= np.array([0,0.265,0.374,0.510,0.546,0.616,0.671,0.753,0.869,1])\n",
    "#p_ref = np.array([366.1,478.1,551.6,613.3,642.2,660.9,672.2,668.1,637.8,587.4]) * kPatommHg\n",
    "#x_ref = np.array([0,0.114,0.180,0.257,0.445,0.658,0.794,0.879,0.956,1])\n",
    "#y_ref= np.array([0,0.208,0.298,0.381,0.537,0.663,0.770,0.847,0.931,1])\n",
    "#p_ref = np.array([1125.2,1362.4,1481,1586.8,1739.2,1798.5,1781.9,1722.3,1635.8,1566.1])*kPatommHg\n",
    "ax.scatter(1-x_ref,p_ref,color='blue',marker='s'\n",
    "           ,label=r\"Ponto de bolha - Rall (1958)\")\n",
    "ax.scatter(1-y_ref,p_ref,color='black',marker='s',\n",
    "           label=r\"Ponto de orvalho - Rall (1958)\")\n",
    "\n",
    "'''exp = pd.read_csv('experimental.csv', sep=';')\n",
    "exp.head()\n",
    "exp['p'] = exp['p']/10\n",
    "exp['p'][2] = 84.881\n",
    "exp['p'][19] = 87.005\n",
    "ax.plot(exp['x1'],exp['p']*kPatommHg,'b--',label=r\"Bubble point - experimental data\")\n",
    "ax.plot(exp['y1'],exp['p']*kPatommHg,'k--',label=r\"Dew point - experimental data\")'''\n",
    "ax.legend(loc=3)\n",
    "ax.set_title('Acetona n-Hexano',fontsize=22)"
   ]
  }
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