PengRobinson_2020_04_03.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## General Peng-Robinson Cubic Equation of State Solver\n",
    "\n",
    "I originally started working on this problem because I wanted a better understanding of how classes worked in Python and wanted to use a problem I already understood to do so. With the benefit of hindsight I _probably_ wouldn't have done it this way, but it's functional so here we are.\n",
    "\n",
    "The [Peng-Robinson Equation of State](https://en.wikipedia.org/wiki/Equation_of_state#Peng%E2%80%93Robinson_equation_of_state) is a cubic equation of state for relating Temperature, Pressure, and vapor density similar to the ideal gas law typically presented in high school chemistry, or the van der Waals equation of state typically presented in freshman chemistry. It does a better job than either of those by introducting terms that give particles volume (ideal gas law assumes point particles), as well as allowing electrostatic interactions between particles.\n",
    "\n",
    "Outline of what's available here:\n",
    "* Setup of python classes for pure components and mixtures of components\n",
    "* Building out a [Full-Factorial](https://en.wikipedia.org/wiki/Factorial_experiment) experiment for determining mole fractions of components based on Temperature and Pressure\n",
    "* A simple neural network of the results using sklearn"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, we need to import libraries:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import scipy.optimize\n",
    "from sklearn.neural_network import MLPRegressor\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "from numpy.linalg import inv\n",
    "import copy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next I was unable to find a cubic solver that I liked, so I wrote my own. This function takes two derived terms from the Peng-Robinson EOS and finds the roots of the equation. Specifically it finds the highest of 3 roots if it exists, which is the factor we need for the vapor phase"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def PengRobinsonCubic(A,B,root=2):\n",
    "        coeff = [A/A,B-1,A-2*B-3*B**2,B**3+B**2-A*B]\n",
    "        a = coeff[0]\n",
    "        b = coeff[1]\n",
    "        c = coeff[2]\n",
    "        d = coeff[3]\n",
    "        \n",
    "        p = (3 * a * c - b ** 2) / (3 * a ** 2)\n",
    "        q = (2 * (b ** 3) - 9 * a * b * c + 27 * (a ** 2) * d) / (27 * a ** 3)\n",
    "        discriminant = 18 * a * b * c * d - 4 * (b ** 3) * d + (b ** 2) * (c ** 2) - 4 * a * (c ** 3) - 27 * (a ** 2) * (d ** 2)\n",
    "        \n",
    "        if discriminant > 0: #there are 3 real roots\n",
    "            return 2 * ((-p / 3) ** (1 / 2)) * np.cos((1 / 3) * np.arccos(((3 * q) / (2 * p)) * ((-3 / p) ** (1 / 2))) - 2 * np.pi * root / 3) - b / (3 * a)\n",
    "        elif p > 0:\n",
    "            return -2 * ((p / 3) ** (1 / 2)) * np.sinh((1 / 3) * np.arcsinh(((3 * q) / (2 * p)) * ((3 / p) ** (1 / 2)))) - b / (3 * a)\n",
    "        else:\n",
    "            return -2 * (np.abs(q) / q) * ((-p / 3) ** (1 / 2)) * np.cosh((1 / 3) * np.arccosh(((-3 * np.abs(q)) / (2 * p)) * ((-3 / p) ** (1 / 2)))) - b / (3 * a)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next we need to worry about all the math behind the Peng-Robinson EOS, which we can do using two classes. One for pure species components and the other for mixtures. The class for mixtures also needs a solver to get a solution for the mole fractions. This is accomplished with scipy.optimize.least_squares and some linear algebra involving mole fractions adding up to 1 and fugacities.\n",
    "\n",
    "The pure species class has optional terms for PSVR2.\n",
    "\n",
    "When the mixture model does not converge, numbers for np.nan will be used instead.\n",
    "\n",
    "For units:\n",
    "* Temperature is in Celcius\n",
    "* Pressure is in Barg\n",
    "* Volume is in L"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "class component:\n",
    "    def __init__(self, Tc, Pc, omega, kappa1=0, kappa2=0, kappa3=0):\n",
    "        self.Tc = Tc\n",
    "        self.Pc = Pc\n",
    "        self.omega = omega\n",
    "        self.kappa1 = kappa1\n",
    "        self.kappa2 = kappa2\n",
    "        self.kappa3 = kappa3\n",
    "        \n",
    "    def setConditions(self,P,T):\n",
    "        P = np.array(P)\n",
    "        T = np.array(T)\n",
    "        Tc = self.Tc\n",
    "        Pc = self.Pc\n",
    "        omega = self.omega\n",
    "        kappa1 = self.kappa1\n",
    "        kappa2 = self.kappa2\n",
    "        kappa3 = self.kappa3\n",
    "        T = T + 273.15\n",
    "        P = P + 1.01325\n",
    "        R = 0.083144626 #(Bar*L)/(mol*K)\n",
    "        self.R = R\n",
    "        \n",
    "        Tr = T / Tc\n",
    "        self.Tr = Tr\n",
    "        \n",
    "        self.kappa0 = 0.378893+1.4897153*omega-.17131848*omega**2+0.0196554*omega**3\n",
    "        self.kappa = self.kappa0 + (kappa1+kappa2*(kappa3-Tr)*(1-np.sqrt(Tr)))        \n",
    "        self.alpha = (1+self.kappa*(1-np.sqrt(Tr)))**2\n",
    "        \n",
    "        self.a = 0.45724*(R**2)*(Tc**2)/Pc\n",
    "        self.b = 0.07780*R*Tc/Pc\n",
    "        \n",
    "        self.A = (self.a*self.alpha*P)/(self.R**2*T**2)\n",
    "        self.B = (self.b*P)/(self.R*T)\n",
    "        \n",
    "        self.Psat = np.exp(np.log(self.Pc)+np.log(10)*(1-1/Tr)*(7+7*self.omega)/3)\n",
    "        \n",
    "        self.Z = PengRobinsonCubic(self.A,self.B)\n",
    "        \n",
    "        self.Vn = self.Z*self.R*T/P\n",
    "\n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "class mixture:\n",
    "    def __init__(self,component1,component2,k=0):\n",
    "        self.component1 = copy.deepcopy(component1)\n",
    "        self.component2 = copy.deepcopy(component2)\n",
    "        self.k = k\n",
    "        \n",
    "    def setMixtureConditions(self,P,T):\n",
    "        P = np.array(P)\n",
    "        T = np.array(T)\n",
    "        self.P = P + 1.01325\n",
    "        self.T = T + 273.15\n",
    "        self.component1.setConditions(P,T)\n",
    "        self.component2.setConditions(P,T)\n",
    "#         initialize the mole fractions using Raoult's law as a starting point\n",
    "        Raoult = np.array([[1,0,self.component1.Psat,0],[1,0,0,self.component2.Psat],[0,1,-P+10**-10,0],[0,1,0,-P+10**-10]])\n",
    "        SolveAgainst = np.array([1,1,0,0])\n",
    "        [self.x1, self.x2, self.y1, self.y2] = SolveAgainst.dot(inv(Raoult))\n",
    "        \n",
    "    def solveMoleFractions(self):\n",
    "        guess = [self.x1, self.y1]\n",
    "        MoleFractions = scipy.optimize.least_squares(self.F,guess)\n",
    "        self.convergance = MoleFractions.success\n",
    "        self.x1, self.y1 = MoleFractions.x\n",
    "        if not(0 <= (self.x1 or self.y1) <= 1):\n",
    "            self.x1, self.y1 = np.nan, np.nan\n",
    "            return [np.nan, np.nan]\n",
    "        elif np.round((self.x1+10**-10)/(self.y1+10**-10),4) == 1:\n",
    "            return [np.nan, np.nan]\n",
    "        else:\n",
    "            return MoleFractions.x\n",
    "       \n",
    "    def F(self,z):\n",
    "        x1 = z[0]\n",
    "        y1 = z[1]\n",
    "        x2 = 1 - x1\n",
    "        y2 = 1 - y1\n",
    "        P = self.P\n",
    "        T = self.T\n",
    "        R = 0.083144626 #(mL*psi)/(mol*K)\n",
    "        aa1 = self.component1.a*self.component1.alpha\n",
    "        aa2 = self.component2.a*self.component2.alpha\n",
    "        aL = self.component1.a*self.component1.alpha*x1**2+2*x1*x2*(1-self.k)*np.sqrt(self.component1.a*self.component2.a*self.component1.alpha*self.component2.alpha)+self.component2.a*self.component2.alpha*x2**2\n",
    "        aV = self.component1.a*self.component1.alpha*y1**2+2*y1*y2*(1-self.k)*np.sqrt(self.component1.a*self.component2.a*self.component1.alpha*self.component2.alpha)+self.component2.a*self.component2.alpha*y2**2\n",
    "        \n",
    "        bL = x1*self.component1.b+x2*self.component2.b\n",
    "        bV = y1*self.component1.b+y2*self.component2.b\n",
    "        \n",
    "        AL = (aL*P)/(R**2*T**2)\n",
    "        BL = (bL*P)/(R*T)\n",
    "        AV = (aV*P)/(R**2*T**2)\n",
    "        BV = (bV*P)/(R*T)\n",
    "        \n",
    "        ZV = PengRobinsonCubic(AV,BV)\n",
    "        ZL = PengRobinsonCubic(AL,BL)\n",
    "        \n",
    "        self.ZV, self.ZL = ZV, ZL\n",
    "\n",
    "        term1L = -np.log(ZL-BL)\n",
    "        term2L1 = (ZL-1)*self.component1.b/bL\n",
    "        term2L2 = (ZL-1)*self.component2.b/bL\n",
    "        term3L = (AL/(BL*np.sqrt(8)))*np.log((ZL+BL*(np.sqrt(2)+1))/(ZL-BL*(np.sqrt(2)-1)))\n",
    "        term3L1 = (2/aL)*((1-x1)*((1-self.k)*np.sqrt(self.component1.a*self.component1.alpha*self.component2.a*self.component2.alpha))+x1*self.component1.a*self.component1.alpha)-self.component1.b/bL\n",
    "        term3L2 = (2/aL)*((1-x2)*((1-self.k)*np.sqrt(self.component1.a*self.component1.alpha*self.component2.a*self.component2.alpha))+x2*self.component2.a*self.component2.alpha)-self.component2.b/bL\n",
    "        \n",
    "        fugL1 = np.exp(term1L + term2L1 - term3L*term3L1)\n",
    "        fugL2 = np.exp(term1L + term2L2 - term3L*term3L2)\n",
    "        \n",
    "        term1V = -np.log(ZV-BV)\n",
    "        term2V1 = (ZV-1)*self.component1.b/bV\n",
    "        term2V2 = (ZV-1)*self.component2.b/bV\n",
    "        term3V = (AV/(BV*np.sqrt(8)))*np.log((ZV+BV*(np.sqrt(2)+1))/(ZV-BV*(np.sqrt(2)-1)))\n",
    "        term3V1 = (2/aV)*((1-y1)*((1-self.k)*np.sqrt(self.component1.a*self.component1.alpha*self.component2.a*self.component2.alpha))+y1*self.component1.a*self.component1.alpha)-self.component1.b/bV\n",
    "        term3V2 = (2/aV)*((1-y2)*((1-self.k)*np.sqrt(self.component1.a*self.component1.alpha*self.component2.a*self.component2.alpha))+y2*self.component2.a*self.component2.alpha)-self.component2.b/bV\n",
    "        \n",
    "        fugV1 = np.exp(term1V + term2V1 - term3V*term3V1)\n",
    "        fugV2 = np.exp(term1V + term2V2 - term3V*term3V2)\n",
    "        \n",
    "        self.fugL1, self.fugL2, self.fugV1, self.fugV2 = fugL1, fugL2, fugV1, fugV2\n",
    "        \n",
    "        Left = np.array([[1,0,fugL1,0],[1,0,0,fugL2],[0,1,-fugV1,0],[0,1,0,-fugV2]])\n",
    "        Right = np.array([1,1,0,0])\n",
    "        Solution = np.array(Right.dot(inv(Left)))\n",
    "        \n",
    "        return (1000*(Solution[0]-x1))**2 + (1000*(Solution[2]-y1))**2\n",
    "        "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To actually use the Peng-Robinson EOS, we need to know 3 properties of each component:\n",
    "* Critical Temperature\n",
    "* Critical Pressure\n",
    "* [Acentric Factor](https://en.wikipedia.org/wiki/Acentric_factor) (which can be derived from the boiling point, commonly written with the greek letter omega)\n",
    "\n",
    "Critical properties can be obtained from [NIST](https://webbook.nist.gov/chemistry/) or other resources."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As an example, let's look at a binary system with carbon dioxide and ethanol at 5 bar and 40C"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The liquid mole fraction of CO2 is 0.06402955460122187\n",
      "The vapor mole fraction of CO2 is 0.9678388087613046\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\NG\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:69: RuntimeWarning: invalid value encountered in log\n",
      "C:\\Users\\NG\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:72: RuntimeWarning: invalid value encountered in log\n"
     ]
    }
   ],
   "source": [
    "CO2 = component(Tc=304.2, Pc=73.80, omega=0.228, kappa1 = 0.04285)\n",
    "Ethanol = component(Tc=514, Pc=63, omega=.644)\n",
    "\n",
    "myMixture = mixture(CO2,Ethanol,k=0)\n",
    "myMixture.setMixtureConditions(P=5, T=40)\n",
    "[LiquidMoleFractionCO2, VaporMoleFractionCO2] = myMixture.solveMoleFractions()\n",
    "\n",
    "print(f'The liquid mole fraction of CO2 is {LiquidMoleFractionCO2}')\n",
    "print(f'The vapor mole fraction of CO2 is {VaporMoleFractionCO2}')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So we've done the special case of one temperature and one pressure, let's work it out across a range. Let's look at temepratures between 0C and 100C, and pressures between 0 barg and 10 barg, and put those data in a pandas dataframe."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Temperature (C)</th>\n",
       "      <th>Pressure (Barg)</th>\n",
       "      <th>x1</th>\n",
       "      <th>y1</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Temperature (C)  Pressure (Barg) x1 y1\n",
       "0              0.0              0.0      \n",
       "1              0.0              1.0      \n",
       "2              0.0              2.0      \n",
       "3              0.0              3.0      \n",
       "4              0.0              4.0      "
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "numSteps = 11\n",
    "\n",
    "Tmin = 0\n",
    "Tmax = 100\n",
    "\n",
    "Pmin = 0\n",
    "Pmax = 10\n",
    "\n",
    "setup = [[Temp, Pressure]\n",
    "         for Temp in np.linspace(Tmin, Tmax, num=numSteps)\n",
    "         for Pressure in np.linspace(Pmin, Pmax, num=numSteps)]\n",
    "\n",
    "dfMoleFractionData = pd.DataFrame(data=setup, columns=['Temperature (C)','Pressure (Barg)'])\n",
    "dfMoleFractionData['x1'] = ''\n",
    "dfMoleFractionData['y1'] = ''\n",
    "\n",
    "dfMoleFractionData.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It's at this point the way the classes are set up doesn't lend itself well to vectorizing the problem. If we could vectorize it, it would be very fast; but a fleeting attempt to modify it showed it to be challenging. For what I'm trying to accomplish here, time isn't critical and the time it would take to allow vectorization is several orders of magnitude higher than how long it takes the script to run.\n",
    "\n",
    "So we'll loop through each combination of Temperature and Pressure and return the mole fractions of CO2."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\NG\\Anaconda3\\lib\\site-packages\\pandas\\core\\indexing.py:189: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame\n",
      "\n",
      "See the caveats in the documentation: http://pandas.pydata.org/pandas-docs/stable/indexing.html#indexing-view-versus-copy\n",
      "  self._setitem_with_indexer(indexer, value)\n",
      "C:\\Users\\NG\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:69: RuntimeWarning: invalid value encountered in log\n",
      "C:\\Users\\NG\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:72: RuntimeWarning: invalid value encountered in log\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Wall time: 15.2 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "for i in np.arange(len(dfMoleFractionData)):\n",
    "    myMixture.setMixtureConditions(dfMoleFractionData['Pressure (Barg)'].iloc[i],dfMoleFractionData['Temperature (C)'].iloc[i])\n",
    "    dfMoleFractionData['x1'].iloc[i], dfMoleFractionData['y1'].iloc[i] = myMixture.solveMoleFractions()\n",
    "    \n",
    "dfMoleFractionData['x2'] = 1 - dfMoleFractionData['x1']\n",
    "dfMoleFractionData['y2'] = 1 - dfMoleFractionData['y1']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Temperature (C)</th>\n",
       "      <th>Pressure (Barg)</th>\n",
       "      <th>x1</th>\n",
       "      <th>y1</th>\n",
       "      <th>x2</th>\n",
       "      <th>y2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>111</th>\n",
       "      <td>100.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>112</th>\n",
       "      <td>100.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>113</th>\n",
       "      <td>100.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>114</th>\n",
       "      <td>100.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>115</th>\n",
       "      <td>100.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>116</th>\n",
       "      <td>100.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>0.0264851</td>\n",
       "      <td>0.655533</td>\n",
       "      <td>0.973515</td>\n",
       "      <td>0.344467</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>117</th>\n",
       "      <td>100.0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>0.0320651</td>\n",
       "      <td>0.695766</td>\n",
       "      <td>0.967935</td>\n",
       "      <td>0.304234</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>118</th>\n",
       "      <td>100.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>0.0376319</td>\n",
       "      <td>0.727079</td>\n",
       "      <td>0.962368</td>\n",
       "      <td>0.272921</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>119</th>\n",
       "      <td>100.0</td>\n",
       "      <td>9.0</td>\n",
       "      <td>0.0431858</td>\n",
       "      <td>0.752134</td>\n",
       "      <td>0.956814</td>\n",
       "      <td>0.247866</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>120</th>\n",
       "      <td>100.0</td>\n",
       "      <td>10.0</td>\n",
       "      <td>0.0487268</td>\n",
       "      <td>0.772629</td>\n",
       "      <td>0.951273</td>\n",
       "      <td>0.227371</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     Temperature (C)  Pressure (Barg)         x1        y1        x2        y2\n",
       "111            100.0              1.0        NaN       NaN       NaN       NaN\n",
       "112            100.0              2.0        NaN       NaN       NaN       NaN\n",
       "113            100.0              3.0        NaN       NaN       NaN       NaN\n",
       "114            100.0              4.0        NaN       NaN       NaN       NaN\n",
       "115            100.0              5.0        NaN       NaN       NaN       NaN\n",
       "116            100.0              6.0  0.0264851  0.655533  0.973515  0.344467\n",
       "117            100.0              7.0  0.0320651  0.695766  0.967935  0.304234\n",
       "118            100.0              8.0  0.0376319  0.727079  0.962368  0.272921\n",
       "119            100.0              9.0  0.0431858  0.752134  0.956814  0.247866\n",
       "120            100.0             10.0  0.0487268  0.772629  0.951273  0.227371"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dfMoleFractionData.tail(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It's also a good idea to plot the data to make sure it looks reasonable. We're also going to remove the numbers where Peng-Robinson didn't converge."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for column in dfMoleFractionData.columns:\n",
    "    dfMoleFractionData[column] = pd.to_numeric(dfMoleFractionData[column], errors ='coerce')\n",
    "\n",
    "PlotWidth = 6\n",
    "for Condition1, Condition2 in ['Pressure (Barg)', 'Temperature (C)'], ['Temperature (C)', 'Pressure (Barg)']:\n",
    "    for MoleFraction in ['x1', 'y1']:\n",
    "    \n",
    "        plt.figure(figsize=(PlotWidth,PlotWidth))\n",
    "        plt.ylim(0,1)\n",
    "        sns.lineplot(x=Condition1, y=MoleFraction, data=dfMoleFractionData, hue=Condition2)\n",
    "        plt.title(f'{MoleFraction} vs. {Condition1}')\n",
    "        plt.legend(bbox_to_anchor=(1,1), loc=\"upper left\")\n",
    "        plt.show()\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Which looks reasonable."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So that was a lot of work to get vapor and liquid mole fractions. We can bypass using Peng-Robinson by fitting a Neural Netork model to the output and just using the results of that. We're building a model on a model, which has problems; but could be computationally time-saving in a down stream application.\n",
    "\n",
    "First we need to scale the Temperature and Pressure to be on a scale of 0 to 1, otherwise the scikit-learn libraries won't work properly on them. There are built in functions to do that, but for the sake of demonstration I wrote my own."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def ScaleTheThing(unscaled):\n",
    "    scaled = (unscaled - unscaled.min()) / (unscaled.max() - unscaled.min())\n",
    "    return scaled\n",
    "\n",
    "def UnScaleTheThing(scaled, unscaled):\n",
    "    unscaled = scaled * (unscaled.max() - unscaled.min()) + unscaled.min()\n",
    "    return unscaled"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can set up an MLPRegressor for both the liquid and the vapor. I'm not going to tune the hyperparemeters here and just leave them at the default values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "myLiquidNN = MLPRegressor(solver='lbfgs')\n",
    "myVaporNN = MLPRegressor(solver='lbfgs')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Liquid Score: 0.9996924476701617\n",
      "Vapor Score: 0.9989100570730125\n"
     ]
    }
   ],
   "source": [
    "dfMoleFractionData.dropna(inplace=True)\n",
    "X_unscaled = dfMoleFractionData[['Temperature (C)', 'Pressure (Barg)']]\n",
    "X = ScaleTheThing(X_unscaled)\n",
    "LiquidMoleFraction = ScaleTheThing(dfMoleFractionData['x1'])\n",
    "VaporMoleFraction = ScaleTheThing(dfMoleFractionData['y1'])\n",
    "\n",
    "myLiquidNN.fit(X=X, y=LiquidMoleFraction)\n",
    "myVaporNN.fit(X=X, y=VaporMoleFraction)\n",
    "\n",
    "print(f'Liquid Score: {myLiquidNN.score(X, LiquidMoleFraction)}')\n",
    "print(f'Vapor Score: {myVaporNN.score(X, VaporMoleFraction)}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Both give strong r^2 values, but once again it's wise to plot it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYoAAAGDCAYAAAA1cVfYAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMi4zLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvIxREBQAAIABJREFUeJzt3XucXHV9//HXm2UxG24LJhazhEsFYhGESORSK4IiwaiQoiIoKmqlaL3bKGktgpeiRFtriyJWFC9cNcao2PhTUZESJbBIDJAauWYjEoUNYBbZJJ/fH+dMcjKZOXt2s2dmdub9fDz2kZlzzpzzmbOb+cz3rojAzMysnh2aHYCZmbU2JwozM8vlRGFmZrmcKMzMLJcThZmZ5XKiMDOzXE4Utt0kHSdpdc7+SyT9SyNjajeSvizpo+nj50ta2aDrhqQDGnGtsZB0vqSvNTuOdudE0WSS7pU0JOlxSb+X9CVJuzQhjp9IeiKN4w+SFkp6+nicOyLOiYiPjMe5WpWksyRtTO/fo5Juk/SyMq4VETdExIyCMf28jBgKXPt4SddLWifp3mbEYOPHiaI1vDwidgGeAzwX+GCT4nh7GscBwC7AJ5sUx0R1U3r/eoEvAtdI2rP6IEk7NjyyxvsTcBkwr9mB2PZzomghETEAfB84BEDS7pK+KOl3kgYkfVRSV7rvLEk/l/RJSY9IukfSSyrnkrS/pJ9JekzSDyVdXLSIHhGDwCLg8Mz5niLp05LWpD+flvSU7Osk/VNaGrlX0msz27PVJsdJWi3pfZIeSt/bGzPHzpF0Rxr3gKR/zOx7i6RVkh6WtFjStMy+kHSOpN+k9+NiSap+b5KmpSW4PTPbZqZxd0s6QNJP02/Cf5B0dZF7VnX/NpF8SPYAf5l5zx+Q9CDwpfS6L0tLHoOS/lfSs6tiujW9D1cDkzL7tqrqkzQ9LQGulfRHSf8l6a+AS4Bj0lLOYHrsU9K/mfvTEuwlknoy55qX/k7WSHpTvfco6VWSbqna9j5Ji9J78MuI+Cpw90j3S9L/SHp71bZfSTo1ffwfkh5IS2q3SHp+nfNsUwWa/i2ekD7eQdK5kn6b3qfNiVzSJElfS7cPSrpZ0l+MFHuncKJoIZKmA3OA/nTT5cAGkm/4M4ETgb/LvOQoYCUwBbgI+GLmw/EK4JfAU4HzgdeNIo6nAqcCqzKb/xk4miR5HAYcydYln73SOPqANwCXSqpXPbIXsHt67JuBiyXtke77IvD3EbErScL8cRrTC4ELgdOApwP3AVdVnfdlJCWyw9LjZldfOCLWADcBr8hsfg3wjYgYBj4C/ADYA9gb+M8676EuJSWGvwMeB36Tec97AvsCZ0t6Dkky+XuS39HngcXpB/lOJIn6q+lrrq2KN3utLuC7JPdjP5J7elVE3AmcQ1rKiYje9CWfAA4i+T0ekB5/Xnquk4B/BF4MHAickPM2FwP7pwmp4sw05tG6Ajgj854OJrlP30s33ZzGu2d67LWSJlWfpIB3AnOBFwDTgEeAi9N9byD5m5xO8vs4BxgawzXaU0T4p4k/wL0kHyiDJP/ZP0vyTfQvgD8DPZljzwCuTx+fBazK7JsMBMkH0j4kCWZyZv/XgK/lxPETYD2wLj3PbcA+mf2/BeZkns8G7k0fH5deb+fM/muAf0kffxn4aObYIWDHzLEPAUenj+8n+fDcrSq+LwIXZZ7vAgwD+6XPA/ibquufW+e9/h3w4/SxgAeAY9PnXwEuBfYe5e/xrPQeDAJ/AJYCJ2Te85PApMzxnwM+UnWOlSQfYscCawBl9v1v1T1cnT4+BlibvZ9VMf0881wkVULPyGw7BrgnfXwZ8PHMvoPS+3pAnff8OeBj6eNnkXzwPqXqmBMqfyc5927XNK590+cfAy7LOf4R4LD08fmkf9fZ+1L1/6vye7gTeFFm39PTv6EdgTel9/jZZf1fn8g/LlG0hrkR0RsR+0bE2yJiiOQbVTfwu7QoPEjyrfNpmdc9WHkQEevTh7uQfFt6OLMNkg9DYHMvpMfTn3/KHPPOiNgdeDZbvlFXTCNJZBX3pdsqHomIP+Xsz/pjRGzIPF+fxg3JN+c5wH1pFdAxta4fEY8DfyT5RlzxYOZx9pzVvkFSJTON5EM5gBvSfe8n+UD9paQVedUvNSxNf49TIuLoiPhhZt/aiHgi83xf4H2V3236+52evs9pwECkn2ap7L3Pmg7cV3U/65lK8oXilsw1/yfdTnrdBzLH17tmxeXAa9JS7OuAayLizwXi2EpEPEZSejg93XQ68PXK/rRK6860OnCQ5Jv/lNFeh+Sefyvz3u8ENpJ8KfsqsAS4Kq12u0hS9xiu0ZacKFrXAyQliinph09vROwWEc8q8NrfAXtKmpzZNr3yIJJeSLukP/9a/eKIWA58lKRKqFKVtYbkP1rFPum2ij0k7Zyzv5CIuDkiTiFJiItISgbbXD+91lOBgTFcY5Ckeuk0kmqnKysfyhHxYES8JSKmkZRsPqvx6R5aPU3zAyTfxnszP5Mj4kqS319f5t5Dcj9reQDYR7UbyKuv+QeS0tyzMtfcPZIGeNLrTs8cX++ayckjlpKUlJ5Pch/HUu1UcSVwRvrFoAe4HpKuwMAHSH5Xe0RShbaOJJlX+xNJIiR9bRdbkiAk9+olVfd8UkQMRMRwRFwQEQcDf01Sjfn67Xg/bcWJokVFxO9IPsw+JWm3tCHuGZJeUOC19wHLgPMl7ZT+53v5KEO4nOTD+uT0+ZXAByVNlTSFpF67unH8gvR6zyf5j3btaC6Yvva1knaPpL3gUZJvfJDUTb9R0uFKGtH/FfhFRNw7yvdVcQXJB8Er0seVGF4lqVKSeoTkw3bjti/fbl8AzpF0lBI7S3qppF1J2lA2AO+UtGPaqHtknfP8kuQD/uPpOSZJel667/fA3mmbB5E0sn8B+HdJT0vfb5+kSlvONcBZkg5Ov2R8qMD7+ArwX8CGiNjcFTf9e51EUipWGtdOOee5juSLwIeBq9NYIamW2kBavSbpPGC3Ouf4P2BSeh+7SdrQsh0uLgE+JmnfNMapkk5JHx8v6dA0uTxKUiVVxu99QnKiaG2vB3YC7iD50PoGSb1qEa8lqX/+I0np4GqSEkohEfEk8BmgMlDuoyTJ53ZgOXBruq3iwTTGNSTVBudExF1Fr5fxOuBeSY+SNCiemcbzozSWb5J8MD6DLVUVY7GYpMH29xHxq8z25wK/kPR4esy7IuIegLQq6rXbnmr0ImIZ8BaSD9lHSDoOnJXue5KkM8FZ6b5XAwvrnGcjyZeAA0jad1anx0PSEWAF8KCkP6TbPpBea2l6j38IzEjP9X3g0+nrVqX/juSrJJ0OqksTx5KUXq4jKZkMkXzxqSmtslpI0qZxRWbXEpKegP9HUhX2BFtXj2XPsQ54G/DfJCXNP5Hcj4r/IPmd/kDSYyTtSEel+/Yi+f/1KEmV1E/Z9otQx9LW1aDWrpR0sbwrIop8SzQrREnX2oeA50TEb0Y63iYmlyjalKTnplVVO6TdHk8hqfM3G09vBW52kmhvpY0QlXQZST31QxFxSI39IikKziHpoXJWRNxaVjwdaC+SovxTSYrfb42I/vyXmBWnZGoOkYxNsDZWWtWTpGNJxgd8pU6imAO8gyRRHAX8R0QcVX2cmZk1V2lVTxHxM+DhnENOIUkikXaz69U4TUJnZmbjp5ltFH1s3XthNVsPnjIzsxbQzFksaw2YqVkPJuls4GyAnXfe+YhnPvOZZcZlZjahDK4f5sFHn2B446a6x2xY9xAb16+r9bk7omYmitVsPQp0b+qM5I2IS0nm32HWrFmxbNmy8qMzM5sAFvUPMH/hcqYM548P/N3l7x7zNZpZ9bQYeH06KvVoYF06GtnMzApasGQlQyMkie1VZvfYK0lmc5yiZI74D5EM5yciLiEZsTmHZAToeuCNtc9kZmb1rBksfzb00hJFRJwxwv4A/qGs65uZtatF/QMsWLKSNYNDSFD2BBudsCSjmVlbWNQ/wPmLVzA4NLx5W9EkEZs2FZmKviYnCjOzCeCDi5bz9aX31+4aWkdP9w7c+ZFkhWR94mW/GuHwujzXk5lZi1vUPzDqJNG9g7jw1GePfGABThRmZi1uwZKVo0oSXRILXnUYc2eOzxhmJwozsxY3MIqeTT3dXXzqtPFLEuA2CjOzltclsbFAq3Vfbw/zZs8Y1yQBThRmZi1vpCTx6VcfPu7JIctVT2ZmLWxR/0DNifGyykwS4BKFmVnLyA6k653cTQRbjZmopa+3p/S4nCjMzFpAZXK/yrxNj6zPTxCQNFzPmz2j7NBc9WRm1gou+M6KUU3u1yVx4amHll7tBE4UZmZNt6h/oFAJoqKMLrB5XPVkZtZkC5asLHxsWV1g8zhRmJk1WZEBdT3dXQ2raqrmqiczsybrUn4H2Ea2R9TiRGFm1kSL+gdyB9Q1uj2iFicKM7MmqXSJrUeiqSWJCicKM7MmGWm9690ndTc9SYAbs83MGiI76npa2nNppPWu140wKrtRnCjMzEpWPep6YHCI+QuXs3tPd+4UHdMaMD1HEU4UZmYlq1XFNDS8kR1yOjs1anqOItxGYWZWokX9A3XHSfzpydrtE83uDlvNicLMrCQj9WqqZ1NEyyQJcKIwMytNXq8mAZO7a38Et0rbRIUThZlZSfJ6NQUwvDHo7tq6oaKV2iYqnCjMzEoyUslgeFOw80470tfbg0gm/GultokK93oyMyvJvNkzeM/Vt5G34vXg0DC3fejEhsU0Fi5RmJmVZO7MvtwkASNPCNgKnCjMzEq0x+Tu3P15EwK2CicKM7OSLOof4PEnNuQe09diPZxqcaIwMyvJgiUrGd6UP4V4q/VwqsWN2WZmJcnrHtuMJU3HyonCzKwk03p7ak7f0dfbw43nvrAJEY2NE4WZ2TjKTie+e0833V1ieOOW6qeJUt2U5URhZjYGtdaXALaaTnxwaJjuHcQek7sZXD+8+biJUN2U5URhZjZKtdaXeM/Vt9HTvQNDw5u2OnZ4UzB5px3pP6+1B9Xlca8nM7NRqjXZXwDrq5JExUgr2bU6Jwozs1Ea7Qd/q80GO1pOFGZmozSaD/6J2HhdzYnCzGyU5s2eQb0ZmvaY3N3ys8GOlhuzzcxy1OrdNHdmH8vue5ivL71/q0n/erq7+NDLnzXhE0M1Jwozszpq9W6qLG360bmHMmvfPWsmkXbjRGFmVket3k1DwxtZsGQlc2f2bf5pd26jMDOro17vpone3XW0nCjMzOqo17tpond3HS1XPZmZVak0YA8MDiHYpsF6ond3HS0nCjOzjOoG7IDNyWIiTQ0+npwozMwy6k3PMdGmBh9PThRm1rFqjZFwA/a2nCjMrGNkE0Pv5G4ef2LD5qVKK2Mkeid388j64W1e22kN2FlOFGbWEarbHmolg6HhjTxlxx3o6e7aqvqpExuws9w91sw6Qq22h1rWDQ1z4amHtt18TdvDJQoz6wi11q6uZVpvT8eMuC7KJQoz6whdqjff6xadXsVUj0sUZtYRNkbU3Sdo60n9tpcThZl1hL7enprVT508PqKoUqueJJ0kaaWkVZLOrbF/H0nXS+qXdLukOWXGY2ada97sGfR0d221zVVNxZRWopDUBVwMvBhYDdwsaXFE3JE57IPANRHxOUkHA9cB+5UVk5l1rkqVUiesHzHeyqx6OhJYFRF3A0i6CjgFyCaKAHZLH+8OrCkxHjPrcO7NNDZlJoo+4IHM89XAUVXHnA/8QNI7gJ2BE0qMx8zaUL2lSm38lJkoavVFq+52cAbw5Yj4lKRjgK9KOiQiNm11Iuls4GyAffbZp5RgzWziqbdU6bL7Hub6u9Y6eYyTMhuzVwPTM8/3ZtuqpTcD1wBExE3AJGBK9Yki4tKImBURs6ZOnVpSuGY20dRbqvTrS+9nYHCIYEvyWNQ/0Jwg20CZieJm4EBJ+0vaCTgdWFx1zP3AiwAk/RVJolhbYkxm1kbqzehaXXVRWefaxqa0qqeI2CDp7cASoAu4LCJWSPowsCwiFgPvA74g6T0kv9uzInJGxZhZx6rVFjGtztiIWjp5mvDtVeqAu4i4jqTLa3bbeZnHdwDPKzMGM5v46rVFvOKIPr55y8BW1U/VS5dWdPI04dvLcz2ZWcur1xZx/V1rt5np9bVH7+OBdePMU3iYWcvLW3Wu1tiIWfvu6S6z48iJwsxaXr22iHrVSR5YN75c9WRmLe/4Z9buFl9vu40vJwoza3nX31W713y97Ta+XPVkZi2lVjfYvDYKK58ThZm1jHrdYHsnd/PI+uFtjneX18Zw1ZOZtYx63WAjcJfXJnKiMLOWUa8qad3Q8DbjJS489VD3bGoQVz2ZWVNl2yR2kGqubT2tt8ddXpvIicLMmqa6TaJWknAVU/M5UZhZ09RqkwDoktgU4VHVLcKJwsyapl6bxKYI7vn4SxscjdXjxmwza5p63Vvd7bW1OFGYWdPMmz3D3V4nAFc9mVnTVNoePNNra3OiMLOmcrfX1ueqJzMzy+VEYWZmuVz1ZGalqDULrKuYJiaXKMxs3FVGXA8MDhEks8C+++rbOPyCH7Cof6DZ4dkoOVGY2birN+J6cGiY+QuXO1lMME4UZjbu8hYUGhreyIIlKxsYjW0vJwozG3cjjaz2ynQTixOFmY27WiOuszxFx8TiXk9mNu4qvZsu+M6KbZYw9RQdE49LFGZWirkz++g/70Q+/erDvTLdBOcShZmVylN0THwuUZiZWS4nCjMzy+WqJzMbFU/N0XmcKMyssMrUHJVR1wODQ8xfuBzAyaKNuerJzAq74DsrtpmawyOt258ThZkVsqh/YJsxERUead3enCjMrJC8UoNHWrc3JwozKySv1OCR1u3NicLMCqlXaujt6XZDdptzojCzQmpN9NfT3cX5Jz+rSRFZo7h7rJkVUik1eAxF53GiMLPCPG9TZ3KiMDPAI66tPicKM/OIa8vlxmwzY8GSlR5xbXU5UZhZ3TESHnFt4ERhZkDv5O5RbbfO4kRhZkSMbrt1FicKM2PdUO3J/uptt87iRGFmdafn8GR/Bu4ea9aRqsdMHP/MqXzzloGtej71dHd5sj8DXKIw6ziVMRMDg0MEyZiJb94ywCuO6KOvtwcBfb09XHjqoR5DYcAYSxSSlkfEoeMdjJmVr96YievvWsuN576wSVFZK6ubKCSdWm8XsFc54ZhZGbJVTfU6MnnMhNWTV6K4Gvg61Py7mlROOGY23qqn56jHDddWT16iuB34ZET8unqHpBPKC8nMxlOtqqZqbri2PHmJ4t3Ao3X2/W0JsZhZCfKqlASeKdZGVDdRRMQNAJL2jIiHq/YtKzswMxsf03p7GKiRLPp6e9x4bYUU6R77C0nXSpojSaVHZGbjqt4Spq5qsqKKJIqDgEuB1wGrJP2rpIOKnFzSSZJWSlol6dw6x5wm6Q5JKyRdUTx0Myti7sw+Ljz1UI+RsDFTjGLWL0nHA18DdgZ+BZwbETfVObYL+D/gxcBq4GbgjIi4I3PMgcA1wAsj4hFJT4uIh/JimDVrVixb5povM7PRkHRLRMway2tHHHAn6anAmSQlit8D7wAWA4cD1wL713npkcCqiLg7Pc9VwCnAHZlj3gJcHBGPAIyUJMzMrPGKVD3dBOwGzI2Il0bEwojYkDZoX5Lzuj7ggczz1em2rIOAgyTdKGmppJNqnUjS2ZKWSVq2du3aAiGbmdl4KTKFx4yoUz8VEZ/IeV2thu/q8+wIHAgcB+wN3CDpkIgYrLrOpSTtJMyaNcsz5JuZNdCIJYp6SaKA1cD0zPO9gTU1jvl2RAxHxD3ASpLEYWZmLaLM2WNvBg6UtL+knYDTSdo2shYBxwNImkJSFXV3iTGZmdkolZYoImID8HZgCXAncE1ErJD0YUknp4ctAf4o6Q7gemBeRPyxrJjMzGz0RuweK2kqSe+k/ci0aUTEm0qNrA53jzUzG71Su8cC3wZuAH4I5M8sZmalqV6VzvMzWaMUSRSTI+IDpUdiZnVVTxU+MDjE/IXLAZwsrHRF2ii+K2lO6ZGYWV31VqVbsGRlkyKyTlIkUbyLJFk8Iemx9Kfe9ONmVoJ6U4V7VTprhBGrniJi10YEYmb11Zsq3KvSWSMU6h4r6WRJn0x/XlZ2UGa2NU8Vbs1UZFLAjwPPJVk/G+Bdkv4mImpOG25mY5PXq6nyr3s9WTMUGUdxO3B4RGxKn3cB/RHx7AbEtw2Po7B2VN2rCZISg9eNsPGyPeMoio7M7s083n0sFzKz+tyryVpZkXEUFwL9kq4nmRH2WGB+qVGZdRj3arJWVqTX05WSfkLSTiHgAxHxYNmBmXUS92qyVjZi1ZOk5wGPRsRiYFfg/ZL2LT0ysw7iXk3WyopUPX0OOEzSYcA84DLgK8ALygzMrN1V93J6xRF9XH/XWvdqspZTJFFsiIiQdArwmYj4oqQ3lB2YWTurNXfTN28ZcC8na0lFej09Jmk+cCbwvbR7bHe5YZm1N/dysomkSKJ4NfBn4M1pI3YfsKDUqMzanHs52URSpNfTg8C/ZZ7fT9JGYWZj5F5ONpEU6fV0qqTfSFon6VHPHmu2/dzLySaSIo3ZFwEvj4g7yw7GrFN47iabSIokit87SZiNXb3J/io/Zq2uSKJYJulqYBFJozYAEbGwtKjM2oSXMLV2UKTX027AeuBE4OXpj9ekMCvA3WCtHRTp9fTGRgRi1o7cDdbaQd1EIen9EXGRpP8Etlm0IiLeWWpkZm3A3WCtHeSVKCoN2F4lyGyM5s2eUXNBIneDtYmkbqKIiO+k/14OIGm35Gk81qDYzCY8d4O1dlBkzexZwJdIphiXpEHgTRFxS9nBmbWyvDWus9wN1ia6It1jLwPeFhE3AEj6G5LE0ZQ1s81agbu9WicpNHtsJUkARMTPAVc/WUdzt1frJHm9np6TPvylpM8DV5L0fno18JPyQzNrXe72ap0kr+rpU1XPP5R5vE13WbNO4m6v1knyej0d38hAzCYSd3u1TlKk19PuJKWJY9NNPwU+HBHrygzMrJW526t1kqK9nn4NnJY+fx1Jr6dTywrKbCJwt1frFEUSxTMi4hWZ5xdIuq2sgMzMrLUU6R47lI6dAEDS8wB37TAz6xBFShRvBS5P2yoAHgHOKi0iMzNrKUWmGb8NOCyd64mI8HrZZmYdJLfqSVKXpCmwOUE8Iektkrw0qplZh6ibKCSdDjwM3C7pp5KOB+4G5gCvbVB8ZmbWZHlVTx8EjoiIVel0HjcBp0fEtxoTmpmZtYK8qqcnI2IVQETcCtzjJGFm1nnyShRPk/TezPNdss8j4t/KC8vMzFpFXqL4AsliRfWem01IRRccMrNE3qSAFzQyELOyLeof4PzFKxgcGt68zQsOmY2syMjszSTdWlYgZmWqrEiXTRIVXnDILN+oEgWgUqIwK1mtFemyvOCQWX2jTRTfKyUKs5KNlAi84JBZfaNKFBHxwbICMStTXiLwgkNm+UZMFJIek/Ro1c8Dkr4l6S8bEaTZ9po3ewY93V3bbN9jcjcXnnqoG7LNchSZPfbfgDXAFSRtFKcDewErSRY1Oq6s4MzGi1ekMxs7RUT+AdIvIuKoqm1LI+JoSb+KiMNKjbDKrFmzYtmyZY28pJnZhCfploiYNZbXFmmj2CTpNEk7pD+nZfblZxkzM5vwiiSK15Ksk/0Q8Pv08ZmSeoC3lxibmZm1gCILF90NvLzO7p+PbzhmZtZqRkwUkqYCbwH2yx4fEW8qLywzM2sVRaqevg3sDvyQZMBd5WdEkk6StFLSKknn5hz3SkkhaUwNLWZmVp4i3WMnR8QHRntiSV3AxcCLgdXAzZIWR8QdVcftCrwT+MVor2FmZuUrUqL4rqQ5Yzj3kcCqiLg7Ip4ErgJOqXHcR4CLgCfGcA0zMytZkUTxLpJk8UQ6KvsxSY8WeF0f8EDm+ep022aSZgLTI+K7eSeSdLakZZKWrV27tsClzcxsvIyYKCJi14jYISImRcRu6fPdCpy71kyzm8ddSNoB+HfgfQViuDQiZkXErKlTpxa4tJmZjZcicz1J0pmS/iV9Pl3SkQXOvRqYnnm+N8lUIBW7AocAP5F0L3A0sNgN2mZmraVI1dNngWOA16TPHydppB7JzcCBkvaXtBPJHFGLKzsjYl1ETImI/SJiP2ApcHJEeH4OM7MWUiRRHBUR/0Da2BwRjwA7jfSiiNhAMnJ7CXAncE1ErJD0YUknb0fMZmbWQEW6xw6nXV0DNg/A21Tk5BFxHXBd1bbz6hx7XJFzWmdY1D/gmV7NWkSRRPEZ4FvA0yR9DHgl4AWMrDSV9a0rS5cODA4xf+FyACcLsyYoMtfT1yXdAryIpCfT3Ii4s/TIrGPVWt96aHgjC5asdKIwa4K6iULSJOAc4ABgOfD5tN3BrFT11rcead1rMytHXmP25cAskiTxEuCTDYnIOl699a3z1r02s/LkJYqDI+LMiPg8SbvEsQ2KyTpcrfWte7q7mDd7RpMiMutseW0Uw5UHEbFBqjXQ2mz8eX1rs9aSlygOy8zpJKAnfS4gCk7jYTYmc2f2OTGYtYi6iSIiuurtMzOzzlFkZLaZmXUwJwozM8tVZGS22bjy9BxmE4sThTWUp+cwm3hc9WQNlTc9h5m1JicKayhPz2E28bjqyRqi0i4RdfZ7eg6z1uVEYaWrbpeo5uk5zFqbE4WVrla7REWfez2ZtTwnCitdvfYHATee+8LGBmNmo+bGbCudpw03m9icKKx0njbcbGJz1ZOVztOGm01sThTWEJ423GzictWTmZnlcqIwM7NcThRmZpbLicLMzHK5Mdvq8roRZgZOFFaH140wswpXPVlNXjfCzCqcKKwmrxthZhVOFFZTvXmYAnjex3/Mov6BxgZkZk3jRGE11ZqfqaLSXuFkYdYZnCisprkz+7jw1EPpq1OycHuFWedworC65s7s48ZzX4jq7Hd7hVlncKKwEXk9CbPO5kRhI/J6EmadzQPubEReT8KsszlRWCFeT8Ksc7nqyczMcjlRmJlZLicKMzPL5URhZma5nCjMzCyXE4WZmeVyojAzs1xOFGZmlsuJwszMcjlRmJlZLicKMzPL5URhZmZF3YrHAAAK5klEQVS5nCjMzCyXE4WZmeVyojAzs1xej2KCW9Q/4AWFzKxUThQT2KL+AeYvXM7Q8EYABgaHmL9wOYCThZmNG1c9TWALlqzcnCQqhoY3smDJyiZFZGbtqNREIekkSSslrZJ0bo3975V0h6TbJf1I0r5lxtNu1gwOjWq7mdlYlJYoJHUBFwMvAQ4GzpB0cNVh/cCsiHg28A3gorLiaUfTentGtd3MbCzKLFEcCayKiLsj4kngKuCU7AERcX1ErE+fLgX2LjGetjNv9gx6uru22tbT3cW82TOaFJGZtaMyG7P7gAcyz1cDR+Uc/2bg+yXG03YqDdbu9WRmZSozUajGtqh5oHQmMAt4QZ39ZwNnA+yzzz7jFV9bmDuzz4nBzEpVZtXTamB65vnewJrqgySdAPwzcHJE/LnWiSLi0oiYFRGzpk6dWkqwZmZWW5klipuBAyXtDwwApwOvyR4gaSbweeCkiHioxFgmJA+mM7NWUFqiiIgNkt4OLAG6gMsiYoWkDwPLImIxsADYBbhWEsD9EXFyWTFNJB5MZ2atotSR2RFxHXBd1bbzMo9PKPP6E1neYDonCjNrJI/MblEeTGdmrcKJokV5MJ2ZtQonihblwXRm1io8e2yL8mA6M2sVThQtzIPpzKwVuOrJzMxyOVGYmVkuJwozM8vlRGFmZrmcKMzMLJcThZmZ5XKiMDOzXE4UZmaWy4nCzMxyOVGYmVkuJwozM8vlRGFmZrmcKMzMLJdnjx0ni/oHPCW4mbUlJ4pxsKh/gPkLl29e43pgcIj5C5cDOFmY2YTnqqdxsGDJys1JomJoeCMLlqxsUkRmZuPHiWIcrBkcGtV2M7OJxIliHEzr7RnVdjOzicSJYhzMmz2Dnu6urbb1dHcxb/aMJkVkZjZ+3Jg9DioN1u71ZGbtyIlinMyd2efEYGZtyVVPZmaWy4nCzMxyOVGYmVkuJwozM8vlRGFmZrmcKMzMLJcThZmZ5XKiMDOzXE4UZmaWy4nCzMxyOVGYmVkuJwozM8vlRGFmZrmcKMzMLJcThZmZ5XKiMDOzXE4UZmaWy4nCzMxyOVGYmVkuJwozM8vlRGFmZrmcKMzMLJcThZmZ5XKiMDOzXE4UZmaWy4nCzMxyOVGYmVkuJwozM8vlRGFmZrmcKMzMLFepiULSSZJWSlol6dwa+58i6ep0/y8k7VdmPGZmNno7lnViSV3AxcCLgdXAzZIWR8QdmcPeDDwSEQdIOh34BPDqsVxvUf8AC5asZM3gENN6e5g3ewZzZ/Zt79swM+t4ZZYojgRWRcTdEfEkcBVwStUxpwCXp4+/AbxIkkZ7oUX9A8xfuJyBwSECGBgcYv7C5SzqH9ie+M3MjHITRR/wQOb56nRbzWMiYgOwDnjqaC+0YMlKhoY3brVtaHgjC5asHO2pzMysSmlVT0CtkkGM4RgknQ2cnT79s6RfZ/fvtNcBR9QK4HeA5q+6ZeRQJ6wpwB+aHUSL8L3YwvdiC9+LLWaM9YVlJorVwPTM872BNXWOWS1pR2B34OHqE0XEpcClAJKWRcSsUiKeYHwvtvC92ML3Ygvfiy0kLRvra8useroZOFDS/pJ2Ak4HFlcdsxh4Q/r4lcCPI2KbEoWZmTVPaSWKiNgg6e3AEqALuCwiVkj6MLAsIhYDXwS+KmkVSUni9LLiMTOzsSmz6omIuA64rmrbeZnHTwCvGuVpLx2H0NqF78UWvhdb+F5s4XuxxZjvhVzTY2ZmeTyFh5mZ5WrZROHpP7YocC/eK+kOSbdL+pGkfZsRZyOMdC8yx71SUkhq2x4vRe6FpNPSv40Vkq5odIyNUuD/yD6SrpfUn/4/mdOMOMsm6TJJD1UPIcjsl6TPpPfpdknPKXTiiGi5H5LG798CfwnsBPwKOLjqmLcBl6SPTweubnbcTbwXxwOT08dv7eR7kR63K/AzYCkwq9lxN/Hv4kCgH9gjff60ZsfdxHtxKfDW9PHBwL3Njruke3Es8Bzg13X2zwG+TzKG7WjgF0XO26olioZN/zEBjHgvIuL6iFifPl1KMmalHRX5uwD4CHAR8EQjg2uwIvfiLcDFEfEIQEQ81OAYG6XIvQhgt/Tx7mw7pqstRMTPqDEWLeMU4CuRWAr0Snr6SOdt1UTRsOk/JoAi9yLrzSTfGNrRiPdC0kxgekR8t5GBNUGRv4uDgIMk3ShpqaSTGhZdYxW5F+cDZ0paTdIT8x2NCa3ljPbzBCi5e+x2GLfpP9pA4fcp6UxgFvCCUiNqntx7IWkH4N+BsxoVUBMV+bvYkaT66TiSUuYNkg6JiMGSY2u0IvfiDODLEfEpSceQjN86JCI2lR9eSxnT52arlihGM/0HedN/tIEi9wJJJwD/DJwcEX9uUGyNNtK92BU4BPiJpHtJ6mAXt2mDdtH/I9+OiOGIuAdYSZI42k2Re/Fm4BqAiLgJmEQyD1SnKfR5Uq1VE4Wn/9hixHuRVrd8niRJtGs9NIxwLyJiXURMiYj9ImI/kvaakyNizHPctLAi/0cWkXR0QNIUkqqouxsaZWMUuRf3Ay8CkPRXJIlibUOjbA2LgdenvZ+OBtZFxO9GelFLVj2Fp//YrOC9WADsAlybtuffHxEnNy3okhS8Fx2h4L1YApwo6Q5gIzAvIv7YvKjLUfBevA/4gqT3kFS1nNWOXywlXUlS1TglbY/5ENANEBGXkLTPzAFWAeuBNxY6bxveKzMzG0etWvVkZmYtwonCzMxyOVGYmVkuJwozM8vlRGFmZrmcKKztSNoo6TZJv5Z0raTJ23Gu4yR9N3188ggz1vZKetsYrnG+pH8cxfGvSmeD3dSmgwmtxThRWDsaiojDI+IQ4EngnOzOdLDRqP/2I2JxRHw855BeklmNy/Zr4FSSGXLNSudEYe3uBuAASftJulPSZ4FbgemSTpR0k6Rb05LHLrB5bYO7JP2c5AOZdPtZkv4rffwXkr4l6Vfpz18DHweekZZmFqTHzZN0czr3/wWZc/1zun7CD4EZ1UFL2lXSPZK60+e7SbpXUndE3BkRK0u7Y2ZVnCisbaVzgL0EWJ5umkEyxfJM4E/AB4ETIuI5wDLgvZImAV8AXg48H9irzuk/A/w0Ig4jmf9/BXAu8Nu0NDNP0okkcysdCRwOHCHpWElHkMwkMJMkET23+uQR8RjwE+Cl6abTgW9GxPBY74fZWLXkFB5m26lH0m3p4xtIpnuZBtyXzsEPyYSBBwM3ptOe7ATcBDwTuCcifgMg6WvA2TWu8ULg9QARsRFYJ2mPqmNOTH/60+e7kCSOXYFvVdYQkVRv6pH/Bt5PMmfTG0nWlzBrOCcKa0dDEXF4dkOaDP6U3QT8v4g4o+q4wxm/6eoFXBgRn6+6xruLXCMibkyrzF4AdEVEzeUtzcrmqifrVEuB50k6AEDSZEkHAXcB+0t6RnrcGXVe/yOSZWeR1CVpN+AxktJCxRLgTZm2jz5JTyNphP5bST2SdiWp5qrnK8CVwJfG8ibNxoMThXWkiFhLssDRlZJuJ0kcz4yIJ0iqmr6XNmbfV+cU7wKOl7QcuAV4Vjoz641pt9wFEfED4ArgpvS4bwC7RsStwNXAbcA3SarH6vk6sAdJsgBA0t+mM4Mek8a5ZGx3wawYzx5r1sIkvRI4JSJe1+xYrHO5jcKsRUn6T5JeW3OaHYt1NpcozMwsl9sozMwslxOFmZnlcqIwM7NcThRmZpbLicLMzHI5UZiZWa7/D8kMHBylVUp2AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(PlotWidth, PlotWidth))\n",
    "plt.xlim(0,1)\n",
    "plt.ylim(0,1)\n",
    "plt.scatter(x=myLiquidNN.predict(X),y=LiquidMoleFraction)\n",
    "plt.xlabel('Predicted x1')\n",
    "plt.ylabel('Peng-Robinson x1')\n",
    "plt.title('Peng-Robinson vs. Predicted x1 values')\n",
    "plt.show()\n",
    "\n",
    "plt.figure(figsize=(PlotWidth, PlotWidth))\n",
    "plt.xlim(0,1)\n",
    "plt.ylim(0,1)\n",
    "plt.scatter(x=myVaporNN.predict(X),y=VaporMoleFraction)\n",
    "plt.xlabel('Predicted y1')\n",
    "plt.ylabel('Peng-Robinson y1')\n",
    "plt.title('Peng-Robinson vs. Predicted y1 values')\n",
    "plt.show()\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally let's put the predicted values back in our DataFrame"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Temperature (C)</th>\n",
       "      <th>Pressure (Barg)</th>\n",
       "      <th>x1</th>\n",
       "      <th>y1</th>\n",
       "      <th>x2</th>\n",
       "      <th>y2</th>\n",
       "      <th>Predicted x1</th>\n",
       "      <th>Predicted y1</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>10.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>0.111839</td>\n",
       "      <td>0.994675</td>\n",
       "      <td>0.888161</td>\n",
       "      <td>0.005325</td>\n",
       "      <td>0.474844</td>\n",
       "      <td>0.997009</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>10.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>0.130713</td>\n",
       "      <td>0.995390</td>\n",
       "      <td>0.869287</td>\n",
       "      <td>0.004610</td>\n",
       "      <td>0.576207</td>\n",
       "      <td>0.997782</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>10.0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>0.149660</td>\n",
       "      <td>0.995925</td>\n",
       "      <td>0.850340</td>\n",
       "      <td>0.004075</td>\n",
       "      <td>0.682564</td>\n",
       "      <td>0.998438</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>10.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>0.168688</td>\n",
       "      <td>0.996342</td>\n",
       "      <td>0.831312</td>\n",
       "      <td>0.003658</td>\n",
       "      <td>0.790976</td>\n",
       "      <td>1.002285</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>10.0</td>\n",
       "      <td>9.0</td>\n",
       "      <td>0.187807</td>\n",
       "      <td>0.996676</td>\n",
       "      <td>0.812193</td>\n",
       "      <td>0.003324</td>\n",
       "      <td>0.893190</td>\n",
       "      <td>1.009951</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>10.0</td>\n",
       "      <td>10.0</td>\n",
       "      <td>0.207029</td>\n",
       "      <td>0.996948</td>\n",
       "      <td>0.792971</td>\n",
       "      <td>0.003052</td>\n",
       "      <td>0.992390</td>\n",
       "      <td>1.017616</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>20.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>0.045347</td>\n",
       "      <td>0.980226</td>\n",
       "      <td>0.954653</td>\n",
       "      <td>0.019774</td>\n",
       "      <td>0.116246</td>\n",
       "      <td>0.945880</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>20.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>0.060692</td>\n",
       "      <td>0.984993</td>\n",
       "      <td>0.939308</td>\n",
       "      <td>0.015007</td>\n",
       "      <td>0.189271</td>\n",
       "      <td>0.958627</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>20.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>0.076043</td>\n",
       "      <td>0.987856</td>\n",
       "      <td>0.923957</td>\n",
       "      <td>0.012144</td>\n",
       "      <td>0.275097</td>\n",
       "      <td>0.968258</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>20.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>0.091403</td>\n",
       "      <td>0.989765</td>\n",
       "      <td>0.908597</td>\n",
       "      <td>0.010235</td>\n",
       "      <td>0.365018</td>\n",
       "      <td>0.977960</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Temperature (C)  Pressure (Barg)        x1        y1        x2        y2  \\\n",
       "16             10.0              5.0  0.111839  0.994675  0.888161  0.005325   \n",
       "17             10.0              6.0  0.130713  0.995390  0.869287  0.004610   \n",
       "18             10.0              7.0  0.149660  0.995925  0.850340  0.004075   \n",
       "19             10.0              8.0  0.168688  0.996342  0.831312  0.003658   \n",
       "20             10.0              9.0  0.187807  0.996676  0.812193  0.003324   \n",
       "21             10.0             10.0  0.207029  0.996948  0.792971  0.003052   \n",
       "24             20.0              2.0  0.045347  0.980226  0.954653  0.019774   \n",
       "25             20.0              3.0  0.060692  0.984993  0.939308  0.015007   \n",
       "26             20.0              4.0  0.076043  0.987856  0.923957  0.012144   \n",
       "27             20.0              5.0  0.091403  0.989765  0.908597  0.010235   \n",
       "\n",
       "    Predicted x1  Predicted y1  \n",
       "16      0.474844      0.997009  \n",
       "17      0.576207      0.997782  \n",
       "18      0.682564      0.998438  \n",
       "19      0.790976      1.002285  \n",
       "20      0.893190      1.009951  \n",
       "21      0.992390      1.017616  \n",
       "24      0.116246      0.945880  \n",
       "25      0.189271      0.958627  \n",
       "26      0.275097      0.968258  \n",
       "27      0.365018      0.977960  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dfMoleFractionData['Predicted x1'] = myLiquidNN.predict(X)\n",
    "dfMoleFractionData['Predicted y1'] = myVaporNN.predict(X)\n",
    "display(dfMoleFractionData.head(10))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From here, one could iterate over the Tc, Pc, Acentric Factor for any 2-component system at a range of temperatures and pressures."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}