{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Aula: Cálculo Simples do Volume Molar e Pressão De Saturação a partir de uma Equação De Estado Cúbica\n",
    "**Objetivo: calcular e desenhar a curva de pressão de saturação...**\n",
    "* Para uma substância pura (e.g, hexano)\n",
    "* Usando uma *equação de estado* cúbica (e.g, van der Waals)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Formulação matemática do problema\n",
    "\n",
    "* Desenha um gráfico ${P}$ contra ${T}$\n",
    "* Em que para cada ${T}$,\n",
    "* Para uma substância pura pré definida \n",
    "  * A ${P}$ correspondente é a **pressão** de equilíbrio líquido-vapor dessa substância naquela **temperatura**: ${P}^\\mathrm{ sat}({T})$\n",
    "  \n",
    "  > **Análise de consistência do problema proposto: análise de graus de liberdade de acordo com a regra das fases de Gibbs**\n",
    "  >* $\\nu^{Gibbs} = {C}-{F}+2$\n",
    "  >* ...........  $= 1-2+2$\n",
    "  >* ...........  $= 1$\n",
    "  >\n",
    "  >**Conclusão:** Um único grau de liberdade: é possível rerpesentar ${P}^\\mathrm{ sat}$ como função de uma variável, no caso, ${T}$, o problema proposto é um problema *bem colocado*."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Pressão de saturação\n",
    "  * ${P}^{\\mathrm{ sat}}$ é a pressão que resolve ${f}^{\\mathrm{ L}}({T},{P}) = {f}^{\\mathrm { V}}({T},{P})$.\n",
    "  * ${f}$ é a fugacidade, que para condição de líquido, é dada por ${f}^\\mathrm{ L}({T},{P})=\\phi({T},\\bar{V}^\\mathrm{ L}) \\times {P}$\n",
    "  * e, para condição de vapor, é dada por ${f}^\\mathrm{ V}$, analogamente.\n",
    "  * E $\\bar{V}^{\\mathrm{ L}}$ e $\\bar{V}^\\mathrm{ V}$ são o volume molar da substância em condição de líquido e de vapor, respectivamente, dados a partir da análise das raízes da solução da equação estado para ${V}$ em função de ${T}$ e ${P}$:\n",
    "  * $\\bar{V}$ são os volumes que resolvem ${P}\\bar{V}^3−({P}{b}+{R}{T})\\bar{V}^2+{a}\\bar{V}−{a}{b}={0}$\n",
    "    * Se 3 raízes no intervalo Real $\\left( b, \\infty \\right)$\n",
    "      * $\\bar{V}^\\mathrm{ L}$ é a menor e $\\bar{V}^\\mathrm{ V}$ é a maior delas.\n",
    "    * Se não\n",
    "      * Não há solução para ${P}^\\mathrm{ sat}$ na temperatura em questão."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# A equação de estado\n",
    "  * A equação de estado é, em sua forma explícita-em-pressão: ${P}=\\frac{{R}{T}}{{\\bar{V}}-{b}}-\\frac{{a}}{{\\bar{V}}^2}$\n",
    "  \n",
    "  * Em que$a$ e $b$ são parâmetros dependentes da substância, dados por\n",
    "    * ${a}=\\frac{27}{64}\\frac{{{Tc}^2}{{R}^2}}{Pc}$\n",
    "    * ${b}=\\frac{{R}{Tc}}{{8}{Pc}}$\n",
    "  * E ${R}$ é a constante dos gases, que em unidades SI possui o valor:\n",
    "    * ${R} = 8.3144598$ $\\mathrm{{J} {\\mathrm{ mol}^{−1}} {\\mathrm{ K}^{−1}}}$\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Propriedades conhecidas da substância\n",
    "* A equação de estado de van der Waals depende de algumas poucas propriedades da substância para fazer sua previsão do comportamento delas em condição de líquido ou vapor\n",
    "  * Temperatura do ponto crítico ${T_c}$\n",
    "    * ${T_c}^{hexano}= 507.50$ $\\mathrm{K}$\n",
    "  * Pressão do ponto crítico ${P_c}$\n",
    "    * ${P_c}^{hexano}= 3010000$ $\\mathrm{Pa}$\n",
    "  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Implementação em python\n",
    "* Fazer as rotinas mais básicas e com operação independente\n",
    "* Testar cada uma delas\n",
    "* Fazer as rotinas de nível mais alto, chamando as básicas (adaptar as básicas conforme necessário)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Constantes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Constante universal - define o sistema de unidades a ser usado no código"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "R = 8.3144598 #J.mol^−1.K^−1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Constantes dependentes dos componentes no sistema:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "Tc = 507.50\n",
    "Pc = 3010000"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Funções de constantes são novas constantes:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# atribui um valor à constante a de acordo com a equação\n",
    "a = 27/64*((Tc**2)*(R**2)/Pc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.4954993637433445\n"
     ]
    }
   ],
   "source": [
    "# confere o valor calculado:\n",
    "print(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0001752320742732558\n"
     ]
    }
   ],
   "source": [
    "# analogamente para b\n",
    "b = (R*Tc)/(8*Pc)\n",
    "print(b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Função básica 1\n",
    "* EoS em representação ${P}({T},\\bar{V})$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# define função para calcular P para valores arbitrários de T e V\n",
    "def function_P(T,V):\n",
    "    # retorna valor da pressão de acordo com a equação:\n",
    "    return R*T/(V-b) - a/(V**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "106510.64263262381\n"
     ]
    }
   ],
   "source": [
    "# como teste, conferimos o resultado de pressão a T ambiente e V de gás ideal\n",
    "print(function_P(298,0.0224))\n",
    "# o resultado obtido é de 106510.64263262381 Pa, aproximadamente 1 atm, dentro da ordem de grandeza esperada para um hidrocarboneto leve"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Função básica 2: Calculadora de volume\n",
    "* Calcular $\\bar{V}$ que resolve ${P}{\\bar{V}^3}−({P}{b}+{R}{T}){\\bar{V}^2}+{a}\\bar{V}−{a}{b}={0}$\n",
    "\n",
    "** $1^a$ raiz real: método de Newton-Raphson:**\n",
    "\n",
    "* ${Res}={c_3}\\bar{V}^3+{c_2}\\bar{V}^2+{c_1}\\bar{V}+{c_0}$\n",
    "* $\\frac{\\partial {Res}}{\\partial {V}}=3{c_3}\\bar{V}^2+2{c_2}\\bar{V}+{c_1}$\n",
    "* $\\bar{V}_1^{[{k}+1]}=\\bar{V}_1^{[{k}]}-\\frac{Res}{ {\\partial {Res}}/{\\partial \\bar{V}} }$\n",
    "\n",
    "** Estimativa inicial: gás ideal:**\n",
    "\n",
    "* $\\bar{V}_1^{[0]} = \\frac{{R}{T}}{P}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Mais duas raízes: Método de redução de ordem de polinômio:**\n",
    "* ${c_3}\\bar{V}^3+{c_2}\\bar{V}^2+{c_1}\\bar{V}+c_0=(\\bar{V}-\\bar{V}_1)({c_4}\\bar{V}^2+{c_5}\\bar{V}+{c_6})$\n",
    "* ...............................................$={c_4}\\bar{V}^3+({c_5}-{c_4}\\bar{V}_1)\\bar{V}^2+({c_6}-{c_5}\\bar{V}_1)\\bar{V}+(-{c_6}\\bar{V}_1)$\n",
    "* ${c_4} = {c_3}$\n",
    "* ${c_5} = {c_2}+{c_4}\\bar{V}_1$\n",
    "* ${c_6} = {c_1}+{c_5}\\bar{V}_1$\n",
    "\n",
    "**Soluçãos das raizes de uma parábola:**\n",
    "* $\\bar{V}_2 = \\frac{-{c_5}+\\sqrt{{c_5}^2-4{c_4}{c_6}}}{2{c_4}}$\n",
    "* $\\bar{V}_3 = \\frac{-{c_5}-\\sqrt{{c_5}^2-4{c_4}{c_6}}}{2{c_4}}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Importar o pacote NumPy para usar as funções *raiz quadrada*, *exponencial*, *logaritmo*, etc..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Definição da função calculadore de volume a partir de um par de valores T, P."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def function_V(T,P):\n",
    "    \n",
    "    #definição dos termos da forma polinomial da equação de estado\n",
    "    c3 = P #coeficiente para v^3\n",
    "    c2 = -(P*b+R*T) #coeficiente para v^2\n",
    "    c1 = a  #ceficiente para v^1\n",
    "    c0 = -a*b  #coeficiente para v^0\n",
    "    \n",
    "    #variáveis de método numérico para busca da 1a raiz\n",
    "    RES=1 #resíduo do método\n",
    "    TOL=1e-9 #tolerância do resíduo\n",
    "    MAX=1000 #número máximo de iterações aceitável\n",
    "    \n",
    "    V1=R*T/P #estimativa inicial\n",
    "\n",
    "    i=0 #contador de iteraçõesm iniciado como zero, incrementado em 1 após cada iteração concluída\n",
    "    while(RES>TOL and i<MAX): #Em caso de problema em que o método iterativo crie um loop infinito\n",
    "                              #interromper o Kernel: Botão \"STOP\", ou Barra de ferramentas > Kernel > Interrupt\n",
    "        V1 -= (c3*V1**3+c2*V1**2+c1*V1+c0)/(3*c3*V1**2+2*c2*V1+c1) #atualização do valor de V por subtração do termo f/df a cada iteração\n",
    "        RES=np.abs(c3*V1**3+c2*V1**2+c1*V1+c0) #cálculo do resíduo com o novo valor de V\n",
    "        i += 1 #incremento no contador de iterações\n",
    "\n",
    "    # cálculo das demais raízes: V2 e V3\n",
    "    \n",
    "    #definição dos termos da forma polinomial da equação de estado reduzida ( dada uma de suas raízes )\n",
    "    c4=c3\n",
    "    c5=c2+c4*V1\n",
    "    c6=c1+c5*V1\n",
    "    \n",
    "    #resolução analítica de parábola\n",
    "    delta=(c5**2)-(4*c4*c6)\n",
    "    \n",
    "    if delta < 0: #caso o termo \"delta\" seja negativo, V2 e V3 são raízes complexas, logo só existe uma raiz real, o que fazer?\n",
    "        V_only = V1 #temos uma única raiz real\n",
    "        return [V_only] #retornamos ela como resultado da calculadora de volume\n",
    "        #obs: retorna o valor de volume envolta em colchetes,\n",
    "        #i.e. na forma de uma lista de um elemento,\n",
    "        #para q o codigo externo q faça uso dessa função possa\n",
    "        #descobrir o numero de raízes a partir da função `len`, veja no teste a seguir:`\n",
    "    \n",
    "    else: #caso contrário, existem mais duas raízes reais, a seguir:\n",
    "        V2=(-c5 + np.sqrt(delta))/(2*c4)\n",
    "        V3=(-c5 - np.sqrt(delta))/(2*c4)\n",
    "\n",
    "    # além do caso de raízes V2 e V3 complexas, é preciso eliminar valores menores q o parâmetro b da equação de estado, pois não representam soluções físicamente coerentes para o volume \n",
    "        # filtrar apenas V no intervalo (b,infnty)\n",
    "        nroots=0\n",
    "        if ((V1>b) and (V2>b) and (V3>b)): #sendo as tres fisicamente coerentes\n",
    "            #usando a função `sort` podemos criar uma lista que, nos casos de três raízes físicas, as apresenta em ordem crescente,\n",
    "            #logo, V_líquida, V_intermediária, V_vapor\n",
    "            [VL,Vi,VV]=np.sort([V1,V2,V3])\n",
    "            return [VL,Vi,VV]\n",
    "        else:\n",
    "            V_only = np.max([V1,V2,V3]) #temos uma única raiz no intervalo (b, infinito)\n",
    "            return [V_only] #retornamos ela como resultado da calculadora de volume\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3  raiz(es):\n",
      "liquid volume =  0.000225711777704\n",
      "vapor volume =  0.0239165476647\n",
      "1  raiz(es):\n",
      "unique volume =  0.04956024274063786\n"
     ]
    }
   ],
   "source": [
    "# testar o resultado da função\n",
    "\n",
    "test_T=298 #vamos testar quais os volumes calculados a T ambiente\n",
    "test_P=1e5 #e P atmosférica\n",
    "\n",
    "# atribui a variável de resposta `ans_V` o resultado do calculo de V nas condições (test_T,test_P)\n",
    "ans_V = function_V(test_T,test_P)\n",
    "\n",
    "# a função `len` retorna o tamanh da lista de volumes, i.e. o número de soluções de volume encontradas\n",
    "print(len(ans_V), \" raiz(es):\")\n",
    "\n",
    "#usando o deferenciador por índice: lista[indice], começando pelo zero, temos acesso ao valor de cada volume\n",
    "\n",
    "if (len(ans_V) == 3 ):\n",
    "    print(\"liquid volume = \", ans_V[0])\n",
    "    print(\"vapor volume = \", ans_V[2])\n",
    "else:\n",
    "    print(\"unique volume = \", ans_V)\n",
    "    \n",
    "test_T=600 #vamos testar quais os volumes calculados a T maor q Tc\n",
    "test_P=1e5 #e P atmosférica\n",
    "\n",
    "ans_V = function_V(test_T,test_P)\n",
    "\n",
    "print(len(ans_V), \" raiz(es):\")\n",
    "\n",
    "if (len(ans_V) == 3 ):\n",
    "    print(\"liquid volume = \", ans_V[0])\n",
    "    print(\"vapor volume = \", ans_V[2])\n",
    "else:\n",
    "    print(\"unique volume = \", ans_V[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Função básica 3\n",
    "* energia de Gibbs residual\n",
    "$${\\bar{G}^\\mathrm{ Res}} = {P}\\bar{V}-{R}{T}-\\frac{a}{\\bar{V}} -{R}{T} \\times ln \\left (\\frac{{P}(\\bar{V}-{b})}{{R}{T}} \\right )$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#define função para energia de Gibbs residual de acordo com a equação\n",
    "def Residual_G(T,P,V):\n",
    "    return (P*V)-(R*T)-(a/V)-T*(R*np.log(P*(V-b)/(R*T)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.00018686631450534036, 0.0028154881548850706, 8.3116326776048819]\n",
      "-2978.36956768\n",
      "4979.68247208\n",
      "-0.282664348816\n"
     ]
    }
   ],
   "source": [
    "test_T=100\n",
    "test_P=100\n",
    "Vs=function_V(test_T,test_P)\n",
    "print(Vs)\n",
    "print(Residual_G(test_T,test_P,Vs[0]))\n",
    "print(Residual_G(test_T,test_P,Vs[1]))\n",
    "print(Residual_G(test_T,test_P,Vs[2]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Método numérico\n",
    "* Cálculo de pressão de saturação de equilíbio líquido vapor de substancia pura baseado no algoritmo apresentado por [Sandler, 1999][Sandler, 3rd, 1999]\n",
    "[Sandler, 3rd, 1999]: https://books.google.com/books?isbn=0471182109"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Substituição sucessiva** \n",
    "\n",
    "$ P^{[k+1]}= \\left[ P\\frac{\\phi^{\\mathrm{L}}(P)}{\\phi^{\\mathrm{V}}(P)} \\right]^{[k]}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def calc_P_sat(T,iguess_P):\n",
    "    \n",
    "    #variáveis de método numérico\n",
    "    RES=1\n",
    "    TOL=1e-9\n",
    "    MAX=1000\n",
    "\n",
    "    #estimativa inicial\n",
    "    P=iguess_P\n",
    "    \n",
    "    #contagem de iterações\n",
    "    i=0\n",
    "    while(RES>TOL and i<MAX): #Kernel > Interrupt (console > Ctrl+C)\n",
    "        ans_V=function_V(T,P)\n",
    "        \n",
    "        if (len(ans_V) == 1): #caso so tenha sido encontrada uma raiz, não será possível calcular P_sat para essa temperatura por esse método\n",
    "            return #return sem variável pois não há solução, o código q chama essa função precisa saber lidar com esse resultado excepcional!\n",
    "        [V_L,_,V_V] = ans_V\n",
    "        phi_L=np.exp(Residual_G(T,P,V_L)/(R*T))\n",
    "        phi_V=np.exp(Residual_G(T,P,V_V)/(R*T))\n",
    "        P=P*(phi_L/phi_V)\n",
    "        RES=np.abs(phi_L/phi_V-1.)\n",
    "        i=i+1\n",
    "    return P"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Psat =  2.7815306137\n",
      "Psat =  84.091792973\n",
      "Psat =  811.77760325\n",
      "Psat =  13738.2253961\n"
     ]
    }
   ],
   "source": [
    "#testes da função calc_P_sat\n",
    "\n",
    "test_P = 100\n",
    "\n",
    "test_T = 100\n",
    "\n",
    "Psat=calc_P_sat(test_T,test_P)\n",
    "print(\"Psat = \",Psat)\n",
    "\n",
    "test_T = 125\n",
    "\n",
    "\n",
    "Psat=calc_P_sat(test_T,test_P)\n",
    "print(\"Psat = \",Psat)\n",
    "\n",
    "test_T = 150\n",
    "\n",
    "\n",
    "Psat=calc_P_sat(test_T,test_P)\n",
    "print(\"Psat = \",Psat)\n",
    "\n",
    "test_T = 200\n",
    "\n",
    "Psat=calc_P_sat(test_T,test_P)\n",
    "print(\"Psat = \",Psat)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Grid, Calc and Plot\n",
    "* Definiremos um grid de valores de temperatura sobre o qual queremos calcular a pressão de saturação\n",
    "* Realizaremos o cálculo para cada ponto do grid, recursivamente\n",
    "* Por fim, utilizaremos ferramentas gráficas do matplotlib para desenhar o gráfico de P_sat x T\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#grid feito usando a função linspace, gera pontos igualmente espaçados em escala linear. No caso: 100 pontos, entre 100 e Tc, inclusive.\n",
    "grid_T=np.linspace(100,Tc,100)\n",
    "grid_P=np.zeros(100)\n",
    "\n",
    "#estimativa inicial para o primeiro cálculo\n",
    "guess_P=100\n",
    "\n",
    "#efetua primeiro calculo\n",
    "grid_P[0]=calc_P_sat(grid_T[0],guess_P) #primeiro ponto\n",
    "\n",
    "#efetua demais cálculos\n",
    "for i in range(1,100): #demais pontos\n",
    "    grid_P[i]=calc_P_sat(grid_T[i],grid_P[i-1])\n",
    "    #print(grid_P[i]) #habilitar essa linha - removendo o símbolo de comentário -- # -- - faz com que os resultados de cada iteração sejam exibidos na seção de impressão da célula"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.7815306137\n",
      "278.173786459\n",
      "nan\n"
     ]
    }
   ],
   "source": [
    "#imprimindo apenas alguns dos resultados\n",
    "print(grid_P[0]) #primeiro ponto\n",
    "print(grid_P[9]) #décimo ponto\n",
    "print(grid_P[99])#último ponto: o calculo de psat não convergiu,\n",
    "#o `return` devido ao sem variável o valor da pressão na lista  grid_P mostra `nan`, que significa \"not a number\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#comparação com correlação de Antoine:\n",
    "def PAntoine_nist(T): #http://webbook.nist.gov/cgi/cbook.cgi?ID=C110543&Mask=4\n",
    "    if T < 177.70:\n",
    "        return 0 #no correlation available\n",
    "    elif T <= 264.93:\n",
    "        A=3.45604\n",
    "        B=1044.038\n",
    "        C=-53.893\n",
    "        return (10**( A - (B / (T + C)) )   )* 10**5\n",
    "    elif T < 286.18:\n",
    "        return 0 #no correlation available\n",
    "    elif T<=342.69:\n",
    "        A=4.00266\n",
    "        B=1171.53\n",
    "        C=-48.784\n",
    "        return (10**( A - (B / (T + C)) )   )* 10**5\n",
    "    else:\n",
    "        return 0 #no correlation available\n",
    "    \n",
    "def PAntoine_ddbst(T): #http://ddbonline.ddbst.com/AntoineCalculation/AntoineCalculationCGI.exe\n",
    "    A=7.01051\n",
    "    B=1246.33\n",
    "    C=232.988\n",
    "    return (10**( A - (B / (T - 273 + C)) )   )* 101325/760.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAkcAAAGHCAYAAAC6Q/beAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nSERERCShzpGIiIhIQp0jERERkcR/AcWTda2ADpBJAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f460808b8d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "#ativar uma figura 1\n",
    "plt.figure(1)\n",
    "\n",
    "legend=[] #iniciador do objeto legenda\n",
    "\n",
    "plt.subplot(121) #activate a subplot\n",
    "plt.title('Pressão de saturação, hexano')\n",
    "\n",
    "#o grafico P x T calculado\n",
    "\n",
    "#filtrar not-a-number e zeros\n",
    "grid_P_real = ~np.isnan(grid_P)\n",
    "filtered_grid_T = grid_T[ np.where( grid_P_real ) ]\n",
    "filtered_grid_P = grid_P[ np.where( grid_P_real ) ]\n",
    "\n",
    "#traçar\n",
    "\n",
    "plt.plot(filtered_grid_T,filtered_grid_P, label='vdW') #label é a etiqueta que será usada na legenda\n",
    "\n",
    "#calcular correlações de Antoine\n",
    "\n",
    "## nist\n",
    "grid_TAntoine_nist_1 = np.linspace(177.7,264.93,100)\n",
    "grid_PAntoine_nist_1 = np.array([ PAntoine_nist(grid_TAntoine_nist_1[i]) for i in range(100) ])\n",
    "\n",
    "grid_TAntoine_nist_2 = np.linspace(286.18,342.69,100)\n",
    "grid_PAntoine_nist_2 = np.array([ PAntoine_nist(grid_TAntoine_nist_2[i]) for i in range(100) ])\n",
    "\n",
    "# traçar\n",
    "plt.plot(grid_TAntoine_nist_1,grid_PAntoine_nist_1, label='nist')\n",
    "plt.plot(grid_TAntoine_nist_2,grid_PAntoine_nist_2, label='nist')\n",
    "\n",
    "## ddbst\n",
    "grid_TAntoine_ddbst = np.linspace(100,Tc,100)\n",
    "grid_PAntoine_ddbst = np.array([ PAntoine_ddbst(grid_TAntoine_ddbst[i]) for i in range(100) ])\n",
    "\n",
    "# traçar\n",
    "\n",
    "plt.plot(grid_TAntoine_ddbst,grid_PAntoine_ddbst, label='ddbst')\n",
    "\n",
    "# opções adicionais do gráfico\n",
    "\n",
    "## limites no eixo x e y\n",
    "plt.xlabel('T (K)')\n",
    "plt.ylabel('P (Pa)')\n",
    "plt.xlim([100,Tc])\n",
    "plt.ylim([0,Pc])\n",
    "\n",
    "plt.legend(loc=0) #exibe legenda na localização \"0\", ver no gráfico:\n",
    "\n",
    "#ativar uma segunda figura\n",
    "plt.figure(1)\n",
    "plt.subplot(122) #activate a subplot\n",
    "\n",
    "plt.title('(escala log)')\n",
    "\n",
    "# mesmos plots em escala log\n",
    "plt.semilogy(filtered_grid_T,filtered_grid_P)\n",
    "plt.semilogy(grid_TAntoine_nist_1,grid_PAntoine_nist_1)\n",
    "plt.semilogy(grid_TAntoine_nist_2,grid_PAntoine_nist_2)\n",
    "plt.semilogy(grid_TAntoine_ddbst,grid_PAntoine_ddbst)\n",
    "plt.xlabel('T (K)')\n",
    "plt.xlim([100,Tc])\n",
    "plt.ylim([100,Pc])\n",
    "\n",
    "\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Conclusões\n",
    "Nesta aula, uma equação de estado cúbica simples foi utilizada para calcular volume, energia de Gibbs residual, coeficientes de fugacidade e a pressão de saturação de um fluido puro. Aqui, a pressão de saturação foi obtida buscando uma solução numérica para a pressão que leva a energia de Gibbs residual igual entre as duas fases. Para tal, essa aula introduziu conceitos de cálculo de equilíbrio de fases e formas simples de implementar os cálculos propostos na linguagem python, utilizando funções matemáticas e estruturas do pacote numpy. Após estudar essa aula, o aluno deve ser capaz de resolver problemas simples em equilibrio de fases e entender os pontos chave cruciais dos métodos numéricos envolvidos."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Referências externas\n",
    "Notas de aula de Abreu C. R. A. (UFRJ > EQ > TPQB), não disponíveis online atualmente."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Créditos\n",
    "* Baseado nas notas de aula de *Termodinâmica Aplicada* de Abreu C. R. A. (UFRJ > EQ > TPQB)\n",
    "* Implementado em ipynb com python 3.5 por Iuri Soter Viana Segtovich\n",
    "* Revisado por Fernando de Azevedo Medeiros"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python [conda root]",
   "language": "python",
   "name": "conda-root-py"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}