ejercicios_python_apllicado.ipynb

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        "<a href=\"https://colab.research.google.com/github/andresf-sierra/python_iq_meetup/blob/master/ejercicios_python_apllicado.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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      "source": [
        "####  ***Andrés F. Sierra***\n",
        "\n",
        "  *Estudiante de Ingeniería Química y Ciencia de Datos*\n",
        "\n",
        "  *Campus Rep 2021* \n",
        "\n",
        "  *Diplomado en Análisis de Datos y Machine Learning en Python*\n",
        "  \n",
        "\n",
        " <!-- badges: start -->\n",
        "[![Andres Sierra](https://img.shields.io/badge/LinkedIn-blue?&logoColor=white)](https://www.linkedin.com/in/andresf-sierra/) \n",
        "[![Andres Sierra](https://img.shields.io/badge/GitHub-green?&logoColor=white)](https://github.com/andresf-sierra)\n",
        "<!-- badges: end -->"
      ]
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        "\n",
        "\n",
        "\n",
        "\n",
        "#**Resolución de sistema de ecuaciones lineales**\n",
        "\n",
        "\n",
        "##Columna de destilación para la separación de metano, etano y propano.\n",
        "\n",
        "- Diagrama de una columna de destilación para la separación gruesa de Metano (M), Etano (E), y Propano (P). Separación de fases por componentes.\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n"
      ]
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      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Prbc6NRF-GfW"
      },
      "source": [
        "Cómo bien sabemos, la destilación tiene que ver con diferentes puntos de ebubllición y más especificamente con la diferencia de volatilidades relativas.\n",
        "\n",
        "A partir de los datos dados podemos plantear un balance de materia.\n",
        "\n",
        "\n",
        "\n",
        "###***Balance de Materia***\n",
        "\n",
        "$$m_{in} = m_{out}$$\n",
        "\n",
        "$$30 kg/s = 0.9m_{1} + 0.3m_{2} + 0.1m_{3}$$\n",
        "\n",
        "$$25 kg/s = 0.1m_{1} + 0.5m_{2} + 0.2m_{3}$$\n",
        "\n",
        "$$10 kg/s = 0.0m_{1} + 0.2m_{2} + 0.7m_{3}$$\n",
        "\n",
        "\n",
        "Tenemos un sistema ecuaciones que bien podríamos resolver con algunos de los muchos métodos que hemos aprendido (o aprenderemos) a lo largo de nuestra formación. Sin embargo este problema de sistemas de ecuaciones lineales lo resolveremos en Python de dos formas; una analítica y una numérica. \n",
        "\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mRRBpOy6FiJk"
      },
      "source": [
        "Lo primero que haremos será **importar las librerías** a usar, usaremos `pandas`, `seaborn`, `matplotlib`, `sympy`, y `numpy`.\n",
        "\n",
        "Recordemos que para importar una librería tienes que usar el comando `import + nombres de la librería`. Sin embargo, para no usar el nombre completo de la librería pdoemos usar sus apodos con el comando `as`, por ejemplo, con `pandas` sería `import pandas as pd`. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "oAETvymL0jF4"
      },
      "source": [
        "import pandas as pd \n",
        "import seaborn as sns\n",
        "from matplotlib import pyplot as plt\n",
        "import sympy\n",
        "import numpy as np"
      ],
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zjE_acL6GuBY"
      },
      "source": [
        "Este siguiente papso es simplemente decorativo, pues con ello lograremos que nuestras gráficas se vean mucho más bonitas."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Ea6dRENc01yM"
      },
      "source": [
        "plt.close('all')\n",
        "plt.style.use('ggplot')\n"
      ],
      "execution_count": 3,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DyhUymxdG3yB"
      },
      "source": [
        "Ahora procederemos a la resolución de nuestras ecuaciones lineales.\n",
        "Empezaremos con la solución analítica.\n",
        "- ### ***Solución analítica***\n",
        "  - Declaramos las variables simbólicas con el método `sympy.symbols` (Cómo hicimos en el Notebook de la primera sesión)\n",
        "  - Asignamos las ecuaciones, igualadas a 0\n",
        "  - Solucionamos el sistema\n",
        "  - Imprimimos la solución"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0gl11tbZ1Gu2"
      },
      "source": [
        "# Declaración de variables simbolicas\n",
        "m1, m2, m3 = sympy.symbols('m1 m2 m3')"
      ],
      "execution_count": 4,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "m_BJkDLGHxE8"
      },
      "source": [
        "# Asignación de ecuaciones (Igualadas a 0)\n",
        "eq1 = 0.9*m1 + 0.3*m2 + 0.1*m3 - 30\n",
        "eq2 = 0.1*m1 + 0.5*m2 + 0.2*m3 - 25\n",
        "eq3 = 0.2*m2 + 0.7*m3 - 10\n"
      ],
      "execution_count": 5,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "s3SYescOIEPF"
      },
      "source": [
        "Para solucionar el sistema de ecuaciones, usaremos el método `sympy.solve`. En este llamaremos a las ecuaciones planteadas anteriormente y a las variables."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Moj4uoewHy2Q",
        "outputId": "9390e092-b69f-45b7-bbc8-da5591a91a5b"
      },
      "source": [
        "# Solucion del sistema de ecuaciones\n",
        "solucion = sympy.solve([eq1,eq2,eq3],[m1,m2,m3])\n",
        "# Impresion de la solucion\n",
        "print(solucion[m1])\n",
        "print(solucion[m2])\n",
        "print(solucion[m3]) "
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "17.8846153846154\n",
            "45.9615384615385\n",
            "1.15384615384615\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "sU8jgHAoI6eo"
      },
      "source": [
        "¡Así de sencillo!\n",
        "Con los valores de las corrientes, ahora puedes saber el valor de tu flujo másico de salida."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "H5Nf54hbJ-qh"
      },
      "source": [
        "Ahora podemos emplear una solución numérica\n",
        "- ### ***Solución numérica***\n",
        "  - Definiremos los coeficientes de los balances y los valores de alimentación en un arreglo numérico de `numpy`, o sea, en una matriz. Esto lo haremos con el método `np.array`.\n",
        "  - Imprimiremos nuestras matrices, así observaremos cómo se conforma nuestro sistemas de ecuaciones planteado en el balance\n",
        "  - Ahora usaremos la función `linalg` algebra lineal y su `solve` para resolver el sistema.  "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DE9mEAWt2KWJ"
      },
      "source": [
        "# Solución numerica\n",
        "Matriz_Balances = np.array([[0.9,0.3,0.1],\n",
        "                            [0.1,0.5,0.2],\n",
        "                            [0.0,0.2,0.7]])\n",
        "Alimentacion = np.array([30.0,25.0,10.0])"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "3h49REqFOBpm",
        "outputId": "3ce33ae6-664f-4c24-d30f-624a3848bad6"
      },
      "source": [
        "# Impresion de las matrices\n",
        "print(Matriz_Balances) \n",
        "print(Alimentacion)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.9 0.3 0.1]\n",
            " [0.1 0.5 0.2]\n",
            " [0.  0.2 0.7]]\n",
            "[30. 25. 10.]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bfcd1QqBOJyS"
      },
      "source": [
        "Para solucionar, debemos importar la función `numpy.linalg as nl` específicamente e ingresar en dicha función los coeficientes y los valores de alimentación.\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "15bqn6WMOE4M",
        "outputId": "5e718bce-1e5a-4155-e657-d64e22dcf9c2"
      },
      "source": [
        "#Solucion\n",
        "import numpy.linalg as nl\n",
        "solucion_2  = nl.solve(Matriz_Balances,Alimentacion)\n",
        "print(solucion_2)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[17.88461538 45.96153846  1.15384615]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pmhXjBg5OoM1"
      },
      "source": [
        "Cómo pueden observar, ambos métodos arrojaron el mismo resultado. Esto es de mucha ayuda porque brinda herramientas diferentes y caminos diferentes a tu resolución de problema."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kYalwZ3kO-16"
      },
      "source": [
        "\n",
        "\n",
        "---\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kYVZZIXZ3w6W"
      },
      "source": [
        "#**Ajuste de ecuaciones algebraicas no lineales a datos experimentales**\n",
        "\n",
        "Durante nuestra formación, experimentación y aplicación de conocimientos vamos a tener que ajustar ecuaciones algebraicas y ajustar esos parámetros a datos experimentales. Cómo la ecuación del $Cp$, las ecuaciones de presiones de vapor, las ecuaciones de entalpía o viscosidad.\n",
        "\n",
        "En este caso, tenemos una ecuación no lineal, **la ecuación de Antoine**. Esta ecuación describe la relación entre la tempratura y la presión de saturación del vapor de sustancias puras.\n",
        "\n",
        "$$log_{10}p = A - \\frac{B}{C+T}$$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fxsTR9Y_REKL"
      },
      "source": [
        "Lo primero que haremos será importar las librerías a usar, en este caso `scipy.optimize` y `pylab`.\n",
        "\n",
        "Definiremos la cantidad de datos a modelar, cómo en este caso no tenemos datos experimentales para cargar lo que haremos será crearlos, creando un vector linealmente espaciado.\n",
        "También definiremos los coeficientes A, B y C de la ecuación de Antoine."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "aBSaxXd04Mt7"
      },
      "source": [
        "from scipy.optimize import curve_fit\n",
        "import pylab\n",
        "# Cantidad de datos experimentales modelados\n",
        "n = 40\n",
        "# Coeficientes de la ecuación de Antoine para el Agua (Wikipedia)\n",
        "A = 8.07131\n",
        "B = 1730.63\n",
        "C = 233.426"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "eBj9vZJyxRjn"
      },
      "source": [
        "Crearemos nuestro vector con `numpy`, especificamente usando el método `np.linspace`. En los parámetros de nuestra función `linspace` definiremos de dónde arranca (20), en dónde termina (90) y en cuantos pasos o cuantas divisiones quiero (n=40).\n",
        "Con `np.zeros`, creamos un vector solo de ceros.\n",
        "Además de eso añadiremos un error a los datos para simular datos experimentales agregando el error con la función de `numpy`, `np.random.rand()`"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vGci_LNwwwak"
      },
      "source": [
        "# Construimos una muestra de datos de temperatura: temperatura (Temperatura), versus presion de vapor (Pvapor)\n",
        "Temperatura = np.linspace(20,90,num=n)\n",
        "Pvapor = np.zeros(n)\n",
        "error = np.random.rand(n)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Ghzhv0ElzEDR"
      },
      "source": [
        "Ahora procederemos a generar un ciclo que nos permitirá calcular los datos experimentales de la ecuación. \n",
        "Primero, con los parámetros de Antoine que tenemos calculamos una presión de vapor. \n",
        "A dicho término definido anteriormente, le sumaremos un error o ruido.\n",
        "Añadir aleatoriedad a los datos es necesario porque de no hacerlo, nos quedará una curva completamente perfecta.\n",
        "\n",
        "Ahora definimos una función que tenga cómo parámetros de entrada la temperatura y los coeficientes A, B y C.\n",
        "Y dentro de la función tenemos otro ciclo dónde para cada presión de vapor en la posición `i` va a ser la ecuación de Antoine despejada en función de $P$."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "eewLr-pSy8nT"
      },
      "source": [
        "for i in range(n):\n",
        "    Pvapor[i] = A - B/(Temperatura[i]+C)\n",
        "    Pvapor[i] = (10**Pvapor[i])+50*(error[i]-0.5)\n",
        "\n",
        "def antoine(temp, a, b, c):\n",
        "  n = temp.size\n",
        "  p = np.zeros(n)\n",
        "  for i in range(n):\n",
        "    p[i] = 10**(a - b/(temp[i]+c))\n",
        "  return p\n",
        "  "
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "51xOrFee95_l"
      },
      "source": [
        "En las ecuaciones no lineales es muy importante tener estimaciones de los parámetros iniciales.\n",
        "Llamaremos a la rutina que nos unirá tanto la función y nos ajusta los parámetros, `curve_fit`. A esta rutina la pasamos: \n",
        "- La función de Antoine\n",
        "- El vector de Temperatura\n",
        "- Los datos experimentales de la presión de vapor\n",
        "- Y la estimación de los parámetros.\n",
        "\n",
        "Si queremos predecir datos usando los parámetros ajustados por `curve_fit`, llamamos la ecuación y utilizamos los parámetros que apaprecen en la salida de la función."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ulBUH_zi3SJY"
      },
      "source": [
        "#Estimados iniciales para la Ec. de Antoine\n",
        "\n",
        "params =[10, 2000, 200]\n",
        "\n",
        "# Rutina de optimización que encuentra los parametros\n",
        "popt, pcov = curve_fit(antoine, Temperatura, Pvapor, p0=params)\n",
        "\n",
        "# Calculo de la estimacion del modelo\n",
        "yfit = antoine(Temperatura, popt[0], popt[1], popt[2])"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_OcKIXgQASwH"
      },
      "source": [
        "Ya tenemos todo, sin embargo, la visualización de nuestros datos siempre es una forma muy importante de interpretar nuestros resultados.\n",
        "Procedemos a graficar."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 287
        },
        "id": "LU1nebScAPPg",
        "outputId": "3489257b-9801-4aa2-95d6-30d70ad70978"
      },
      "source": [
        "# Plot de los datos modelados y experimentales\n",
        "pylab.plot(Temperatura,Pvapor,'o',Temperatura, yfit)\n",
        "pylab.xlabel('Temperatura [$ ̂ °C$]')\n",
        "pylab.ylabel('$P ̂ $v [mm Hg]')\n",
        "pylab.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "AElZLayMAl8L"
      },
      "source": [
        "Noten cómo podemos ver los 40 datos, sin embargo, no se ajustan del todo a la línea. Eso es por la aleatoriedad que le añadimos, o el ruido. Esto representa un acercamiento a los datos tomados en laboratorios.\n",
        "En conclusión, podemos observar cómo el modelo logra representar y seguir los datos y nos entrega los parámetros óptimos. "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DcOn6nIMBaTx"
      },
      "source": [
        "\n",
        "\n",
        "---\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "sdts6vM-71wZ"
      },
      "source": [
        "#**Resolución ecuaciones no lineales**\n",
        "\n",
        "\n",
        "Ecuaciones coonstitutiva\n",
        "\n",
        "EOS SRK\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "BEuBpXrz8oRi",
        "outputId": "e53b972a-6c71-4310-b8e0-e36e48924100"
      },
      "source": [
        "#%% Resolución de ecuaciones no lineales\n",
        "import math\n",
        "import scipy.optimize\n",
        "\n",
        "# Funcion que contiene la estructura no lineal de la EOS SRK\n",
        "def SRK(V):\n",
        "    # Propiedades para el monoxido de carbono\n",
        "    T = 300 # K\n",
        "    P = 10 # atm\n",
        "    Tc = 133.0 # K\n",
        "    Pc = 34.5 # atm\n",
        "    w = 0.049 # Factor acéntrico for CO\n",
        "    R = 0.08206 # L atm / (mol K)\n",
        "    a = 0.42747*(R*Tc)**2 / (Pc)\n",
        "    b = 0.08664*(R*Tc/Pc)\n",
        "    m = 0.48508+1.55171*w-0.1561*w**2\n",
        "    alpha = (1+m*(1-math.sqrt(T/Tc)))**2\n",
        "    term1 = R*T/(V-b)\n",
        "    term2 = alpha*a/(V*(V+b))\n",
        "    return P-term1+term2\n",
        "\n",
        "V = 2.0 # L/mol, Estimado inicial\n",
        "# Función de optimización que calcula el valor del volumen\n",
        "V = scipy.optimize.broyden1(SRK, V, maxiter=100, f_tol=1e-6)\n",
        "print(V) # (L)\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "2.4588989615210477\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "G1WOsKfo-CZi"
      },
      "source": [
        "#**Resolución de problemas de valor inicial**\n",
        "\n",
        "Michaelis-Menten\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "id": "UbCVx0IdBcah",
        "outputId": "9353dc59-6c1e-4dba-e3b2-33ca389acec8"
      },
      "source": [
        "#%% Integracion de ecuaciones diferenciales\n",
        "# Metodo de Euler\n",
        "import numpy as np\n",
        "import pylab\n",
        "\n",
        "# Parametros del modelo cinetico\n",
        "Vmax = 2.0  # [mol/(L*s)]\n",
        "Km = 0.5    # [mol/L]\n",
        "\n",
        "# Definición de la EDO\n",
        "def df(s,t):\n",
        "    dsdt = -Vmax*s /(Km+s)\n",
        "    return dsdt\n",
        "\n",
        "# Discretización del tiempo\n",
        "n = 100                     # Pasos en el tiempo\n",
        "t = np.linspace(0,2.0,n)\n",
        "dt = t[1]-t[0]              # DeltaT\n",
        "\n",
        "# Prelocalizar el vector de la solucion y establecer las condiciones iniciales\n",
        "sol = np.zeros(n)\n",
        "sol[0] = 1.0 # initial S in mol / L\n",
        "\n",
        "for i in range(1,n):\n",
        "    sol[i] = sol[i-1]+ dt*df(sol[i-1],t[i-1])\n",
        "\n",
        "# Figuras de resutados\n",
        "plt.close('all')\n",
        "plt.style.use('ggplot')\n",
        "pylab.plot(t,sol)\n",
        "pylab.xlabel(\"tiempo [s]\")\n",
        "pylab.ylabel(\"Concentración [mol/L]\")\n",
        "pylab.show()\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "output_type": "display_data"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Zd_UK4XDDXkI"
      },
      "source": [
        ""
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "id": "KqDfwnouDatF",
        "outputId": "18dad0ac-ab3a-4ac9-dc9d-16e0b6d13d61"
      },
      "source": [
        "#%% Integración con rutinas de scipy\n",
        "import numpy\n",
        "from scipy.integrate import odeint\n",
        "\n",
        "# Definición de la EDO\n",
        "def df(c,t):\n",
        "    s = c[0] # substrate concentration\n",
        "    p = c[1] # product concentration\n",
        "    dsdt = -Vmax*s /(Km + s)\n",
        "    dpdt = Vmax*s /(Km + s + p)\n",
        "    return np.array([dsdt,dpdt])\n",
        "\n",
        "# Condiciones inciales y tiempo de integración\n",
        "c0 = numpy.array([1.0, 0.0]) # [mol / L]\n",
        "t = numpy.linspace(0,2.0,n)\n",
        "\n",
        "# Integracion del modelo\n",
        "sol = odeint(df, c0, t)\n",
        "\n",
        "pylab.plot(t,sol)\n",
        "pylab.xlabel(\"tiempo [s]\")\n",
        "pylab.ylabel(\"Concentración [mol/L]\")\n",
        "pylab.show()\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "output_type": "display_data"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "r1DEJ0IIDaE4"
      },
      "source": [
        "#**Resolución de problemas con condiciones de borde en estado estacionario**\n",
        "\n",
        "\n",
        "- Método de las diferencias finitas: requiere dividr el dominio, a menor igual que x y menos igual que b en un conjunto de puntos discretos o nodos con sus localizaciones dadas por xi. \n",
        "\n",
        "$\\frac{d^2y}{dx^2} + a(x) \\frac{dx}{dx} +b(x) \\cdot y = c(x),$\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 316
        },
        "id": "sIZELb71FZfi",
        "outputId": "825558cc-bbca-4f26-e245-ce9cb20fd253"
      },
      "source": [
        "from numpy.linalg import solve\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "# Funcion que contiene el mallado de la ecuacion DF-RX en EE para coordenadas cilindricas\n",
        "def perfil_concentracion(phi):    \n",
        "    N = 99 # Numero de intervalos\n",
        "    \n",
        "    # Espaciamiento de puntos de diferencia finita\n",
        "    r = np.linspace(0,1.0,N+1)\n",
        "    h = r[1]-r[0]\n",
        "    \n",
        "    # Matriz y vector columna que representan a la geomtria\n",
        "    A = np.zeros((N+1,N+1))\n",
        "    b = np.zeros(N+1)\n",
        "    \n",
        "    # Condición de borde de simetría en r=0\n",
        "    A[0,0] = -1.0\n",
        "    A[0,1] = 1.0\n",
        "    b[0] = 0.0\n",
        "    \n",
        "    # Bucle central de calculo para todos los nodos\n",
        "    for i in range(1,N):\n",
        "        A[i,i-1] = 1.0 - h/r[i]\n",
        "        A[i,i] = -2.0 - phi**2 * h**2\n",
        "        A[i,i+1] = 1.0 + h/r[i]\n",
        "        b[i] = 0.0\n",
        "    \n",
        "    # Condición de borde en r = 1\n",
        "    A[N,N] = 1.0\n",
        "    b[N] = 2.0\n",
        "    c = solve(A,b)\n",
        "    \n",
        "    return ([c,r])\n",
        "\n",
        "# Calculos para cada uno de los modulos de Thiele\n",
        "c,r = perfil_concentracion(1)\n",
        "c3,r3 = perfil_concentracion(3)\n",
        "c5,r5 = perfil_concentracion(5)\n",
        "c10,r10 = perfil_concentracion(10)\n",
        "\n",
        "# Figuras de resultados\n",
        "plt.plot(r,c,r3,c3,r5,c5,r10,c10)\n",
        "plt.xlabel('Radio (Ad)')\n",
        "plt.ylabel('Concentración (Ad)')\n",
        "plt.title('EDP RX-DF en catalizador esférico en EE')\n",
        "plt.legend('','')\n",
        "plt.legend([\"$\\phi = 1$\", \"$\\phi = 3$\", \"$\\phi = 5$\", \"$\\phi = 10$\"], loc =\"lower right\")\n",
        "\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7f4b5e2a3cd0>"
            ]
          },
          "execution_count": 21,
          "metadata": {
            "tags": []
          },
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "output_type": "display_data"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "muYbBXQIIIlj"
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HdMKohRRLxM3"
      },
      "source": [
        "#**Resolución EDO acopladas con ecuaciones algebraicas constitutivas**\n",
        "\n",
        "- Obtención de metil acetato a partir de ácido acético y metanol (destilación reactiva)\n",
        "\n",
        "Parámetros y condciones iniciales\n",
        "\n",
        "- Peso molecular de cada parámetro\n",
        "- Densidad\n",
        "- Temp Reducida\n",
        "- T del sistema\n",
        "- P del sistema\n",
        "- Moles iniciales del acido acético\n",
        "- Concentración\n",
        "- Flujo\n",
        "\n",
        "\n",
        "**Ecuaciones diferenciales**\n",
        "\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 547
        },
        "id": "o_vA6QtUNg63",
        "outputId": "9117072e-f487-4a60-9941-778afaea2a53"
      },
      "source": [
        "#%% Ecuaciones diferenciales acopladas con ecuaciones alebraicas\n",
        "# from scipy import optimize\n",
        "from scipy import integrate\n",
        "\n",
        "# Definicion de parametros y condiciones iniciales\n",
        "N_AA_0=300                  # Moles iniciales de acido acetico (AA) [kmol]\n",
        "MW_AA=60                    # Peso molecular (AA) [g/mol] \n",
        "rho_AA=106.9                # Densidad AA [g/cm3]\n",
        "MW_AAMe=74.1                # Peso molecular metil acetato (AAMe) [g/mol]\n",
        "rho_AAMe=943.4              # Densidad AA_Me [g/cm3]\n",
        "T=300                       # Temperatura [K]\n",
        "T_r=T/506.5                 # Temperature reducida\n",
        "P_tot=101                   # Presion [kPa]\n",
        "V_0=N_AA_0*MW_AA/rho_AA     # Volumen inicial en el reactor [cm3]\n",
        "\n",
        "# Variables\n",
        "k=(8.8E8)*np.exp(-7032.1/T)\n",
        "K_eq=5.2*np.exp(-(8000/1.978)*(1/298-1/T))\n",
        "P_vap=4750*np.exp(10.703-(11.0088/T_r)-5.431*np.\n",
        "log(T_r)+0.3058*T_r**6)\n",
        "\n",
        "\n",
        "#  La lista vacía N se crea para guardar la variación del número de moles de cada componente \n",
        "# en los cuatro primeros lugares y la variación del volumen en la última posición\n",
        "N=[(),(),(),(),()]\n",
        "# La lista vacía Conc se crea para guardar la variación de concetración\n",
        "Conc=[(),(),(),()]\n",
        "# Se define una función que recoge las ecuaciones a resolver\n",
        "\n",
        "\n",
        "def kinetics (N,t):\n",
        "    \n",
        "    # Cálculo de la concentración de cada componente\n",
        "    Conc[0]=N[0]/N[4]\n",
        "    Conc[1]=N[1]/N[4]\n",
        "    Conc[2]=N[2]/N[4]\n",
        "    Conc[3]=N[3]/N[4]\n",
        "    \n",
        "    # Velocidad de reacción del ácido acético\n",
        "    r_AA=k*(Conc[1]*Conc[0]-Conc[3]*Conc[2]/K_eq)\n",
        "    \n",
        "    # Ecuaciones consitutivas\n",
        "    x_AAMe=N[3]/(N[0]+N[1]+N[2]+N[3])   # Fracción molar de metil acetato\n",
        "    F_AAMe=x_AAMe*P_vap/P_tot           # Flujo de metil acetato eliminado\n",
        "    v_0=1                               # Caudal volumétrico de entrada\n",
        "    C_MetOH_0=5                         # Concentración inicial de MetOH\n",
        "    F_MetOH_0=v_0*C_MetOH_0             # Flujo molar de entrada de MetOH\n",
        "    alpha=MW_AAMe/rho_AAMe              # Parametro alpha\n",
        "    \n",
        "    # Ecuaciones diferenciales\n",
        "    # Prelocalizacion del vector solucion\n",
        "    dNdt=np.zeros(5)\n",
        "    \n",
        "    dNdt[0] = -r_AA*N[4]\n",
        "    dNdt[1] = -r_AA*N[4]+F_MetOH_0\n",
        "    dNdt[2] = r_AA*N[4]\n",
        "    dNdt[3] = r_AA*N[4]-F_AAMe\n",
        "    dNdt[4] = v_0-F_AAMe*alpha\n",
        "    return dNdt\n",
        "\n",
        "\n",
        "# Creación de la matriz de tiempo sobre las ecuaciones se evaluará\n",
        "t=np.linspace(0,100,500)\n",
        "# Condiciones iniciales\n",
        "N_ini=[N_AA_0, 0, 0, 0, V_0]\n",
        "# Rutina de integración de sistemas EDOE\n",
        "Res=integrate.odeint(kinetics,N_ini,t)\n",
        "\n",
        "# Figuras de resultados\n",
        "fig,axes=plt.subplots()\n",
        "axes.plot(t,Res[:,0],'b', label='Ácido acetico')\n",
        "axes.plot(t,Res[:,1],'g', label='Metanol')\n",
        "axes.plot(t,Res[:,2],'r', label='Agua')\n",
        "axes.plot(t,Res[:,3],'c', label='Metil acetato')\n",
        "axes.set_xlabel('tiempo [min]')\n",
        "axes.set_ylabel('M [kmol]')\n",
        "axes.grid('on') # Activar grilla\n",
        "legend = axes.legend(loc='best', fontsize='medium') # Leyenda\n",
        "\n",
        "# Variacion del volumen \n",
        "fig,axes=plt.subplots()\n",
        "axes.plot(t,Res[:,4],'k', label='Volumen')\n",
        "axes.set_xlabel('tiempo [min]')\n",
        "axes.set_ylabel('V [cm$^3$]')\n",
        "axes.grid('on')\n",
        "legend = axes.legend(loc='best', fontsize='medium')\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "data": {
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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "output_type": "display_data"
        }
      ]
    }
  ]
}