M1_ultrafiltration-partiel.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#  Nanofiltration de jus de fruit\n",
    "\n",
    "La concentration d’un jus de fruit est réalisée par nanofiltration1 sur une membrane tubulaire de 6 mm de diamètre et de 1,2 m de longueur. La nanofiltration est réalisé en mode tangentielle (cross-flow filtration) c'est à dire avec une vitesse de circulation dans le tube (parrallèle à la membrane) et une vitesse de perméation (perpendiculaire à la membrane). Le jus de fruit a une concentration massique de 0,2 % et est retenu totalement par la membrane.\n",
    "\n",
    "*Données :*\n",
    "- *Jus de fruit à 0.2% massique : $\\rho$=1200 kg/m3, $\\mu$=0,001 Po, D=7.10-10 m2.s-1*\n",
    "- *Pression osmotique du jus de fruit : $\\Pi(bar)=\\frac{133.75c}{100-c}$  avec c concentration en % massique*\n",
    "\n",
    "1 ces calculs peuvent aussi être utilisés pour de l'ultrafiltration ou de l'osmose inverse\n",
    "\n",
    "\n",
    "**1. En considérant l’accumulation du jus de fruit à la surface de la membrane, calculer la concentration en jus de fruit à la surface de la membrane, cm, pour un flux de perméation de 10-6 m/s et 2.10-6 m/s et des vitesses de circulation de 0,05 et 0,1 m/s. Commenter les résultats.**\n",
    "\n",
    ">Lors de la filtration, il y a un couplage entre la convection due à la perméation, J, qui amène les solutés (ou les colloïdes) vers la membrane et la diffusion, D, dans la couche limite, $\\delta$, qui engendre un \"retro\"-transport depuis la membrane vers la solution (ou la dispersion). On peut démontrer (voir cours) en réalisant un bilan différentiel sur un élément de volume dans la couche limite que le profil de concentration est exponentiel :\n",
    "$$c=c_b e^{Jx/D}$$\n",
    ">La concentration à la membrane, $c_m$, est alors :\n",
    "$$c_m=c_b e^{Pe}$$\n",
    ">où, $Pe=\\frac{J\\delta}{D}$, est le nombre de Péclet qui caractérise le rapport entre $\\frac{le~flux~advectif}{le~flux~diffusif}$. Pour calculer le nombre de Péclet il est nécessaire d'estimer l'épaisseur de la couche limite. Il est possible de l'estimer à partir d'une corrélation entre nombre sans dimensions pour le transfert dans un tube.\n",
    "$$Sh=1.86(Re~Sc~\\frac{d_H}{L})^{0.33}$$ pour Re<2100\n",
    "$$Sh=0.023Re^{0.8}Sc^{0.33}$$ pour Re>2100\n",
    "> Le code suivant permet de :\n",
    ">1. calculer l'épaisseur de couche limite\n",
    ">2. caculer le nombre de Péclet\n",
    ">3. calculer la concentration à la membrane"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "L'épaisseur de couche limite est de 256.7 micromètres pour une vitesse tangentielle de  0.05 m/s\n",
      "L'épaisseur de couche limite est de 204.2 micromètres pour une vitesse tangentielle de  0.1 m/s\n",
      "\n",
      "   J   \\   u    |              0.05                0.1\n",
      "------------------------------------------------------------------------------\n",
      "                |       Pe=    0.733               0.583\n",
      "  2.00e-06      |          \n",
      "                |       cm=    0.416               0.358\n",
      "------------------------------------------------------------------------------\n",
      "                |       Pe=    1.834               1.459\n",
      "  5.00e-06      |          \n",
      "                |       cm=    1.251               0.86\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.optimize import newton\n",
    "#DATA\n",
    "#Solution\n",
    "c0=0.2 #% massique\n",
    "D=7.e-10 #m2/s\n",
    "ro=1000 #kg m-3\n",
    "mu=0.001 #Pa.s\n",
    "#membrane\n",
    "d_H=6e-3 #m\n",
    "L=1.2 #m\n",
    "# conditions hydrodynamiques\n",
    "u=[0.05, 0.1] #m/s\n",
    "J=[2.e-6,5.e-6] #m/s\n",
    "\n",
    "#Calcul de l'épaisseur de couche limite, du nombre de Péclet et de la concentration à la membrane\n",
    "deltal=np.zeros(len(u))\n",
    "Re=np.zeros(len(u))\n",
    "Sh=np.zeros(len(u))\n",
    "Pe=np.zeros(len(u)*len(J))\n",
    "cm=np.zeros(len(u)*len(J))\n",
    "Sc=mu/(ro*D)\n",
    "\n",
    "for i in range(len(u)):\n",
    "    Re[i]=ro*u[i]*d_H/mu\n",
    "    if Re[i]<2100:\n",
    "        Sh[i]=1.86*(Re[i]*Sc*d_H/L)**0.33\n",
    "    else:\n",
    "        Sh[i]=0.023*Re[i]**0.8*Sc**0.33\n",
    "    deltal[i]=d_H/Sh[i]\n",
    "    print ('L\\'épaisseur de couche limite est de', round(deltal[i]*1e6, 1),'micromètres pour une vitesse tangentielle de ', u[i],'m/s' )\n",
    "    for j in range(len(J)):\n",
    "        Pe[i+len(u)*j]=J[j]*deltal[i]/D\n",
    "        cm[i+len(u)*j]=c0*np.exp(Pe[i+len(u)*j])\n",
    "print()  \n",
    "print ('   J   \\   u    |             ', round(u[0],3),'              ', round(u[1],3))\n",
    "print ('------------------------------------------------------------------------------')\n",
    "print ('                |       Pe=   ', round(Pe[0],3), '             ', round(Pe[1],3))\n",
    "print (' ', \"%.2e\"%J[0],'     |          ')\n",
    "print ('                |       cm=   ', round(cm[0],3), '             ', round(cm[1],3))\n",
    "print ('------------------------------------------------------------------------------')\n",
    "print ('                |       Pe=   ', round(Pe[2],3), '             ', round(Pe[3],3))\n",
    "print (' ', \"%.2e\"%J[1],'     |          ')\n",
    "print ('                |       cm=   ', round(cm[2],3), '             ', round(cm[3],3))\n",
    "\n",
    "#Tracé du profil de concentration près de la membrane\n",
    "x0=np.linspace(-deltal[0],0,100)\n",
    "x1=np.linspace(-deltal[1],0,100)\n",
    "c_0=c0*np.exp(Pe[0]*(1+x0/deltal[0]))\n",
    "c_1=c0*np.exp(Pe[1]*(1+x1/deltal[1]))\n",
    "c_2=c0*np.exp(Pe[2]*(1+x0/deltal[0]))\n",
    "c_3=c0*np.exp(Pe[3]*(1+x1/deltal[1]))\n",
    "plt.plot(x0,c_0, label='u=0.05 m/s  J=2 um/s') \n",
    "plt.plot(x1,c_1, label='u=0.1 m/s   J=2 um/s')\n",
    "plt.plot(x0,c_2, label='u=0.05 m/s  J=5 um/s')\n",
    "plt.plot(x1,c_3, label='u=0.1 m/s   J=5 um/s')\n",
    "plt.legend(loc='upper center')\n",
    "plt.title('Evolution de la concentration au voisinage de la membrane')\n",
    "plt.xlabel('Distance à la surface de la membrane en mètre')\n",
    "plt.ylabel('Concentration du jus de fruit en % massique')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    ">On note que l'augmentation du flux de perméation engendre une accumulation à la membrane plus importante. Par contre, l'augmentation de la vitesse tangentielle permet de réduire l'accumulation à la membrane. On appelle d'ailleurs cette vitesse la vitesse de balayage tangentiel car elle permet de réduire l'accumulation à la membrane : l'épaisseur de couche limite est plus petite ce qui favorise le transfert de matière par diffusion vers la solution. Mais il faut noter que l'augmentation de la vitesse tangentielle nécessite de l'énergie : il faut donc trouver un compromis."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Le flux de solvant à travers la membrane est directement relié à la concentration à la surface du filtre par la relation suivante : \t\t\t \n",
    "$$J=\\frac{\\Delta P-\\Delta\\Pi}{\\mu R_m}$$\n",
    "où \t\n",
    "- $\\Delta P$ est la différence de pression à travers la membrane\n",
    "- $\\Delta\\Pi$ est la différence de pression osmotique à travers la membrane qui s'écrit $\\Pi(c_m)-\\Pi(c_p)=\\Pi(c_m)$ si la membrane ne retient par le soluté\n",
    "- $R_m$ est la résistance hydraulique de la membrane = 1.10+14 m-1\n",
    "\n",
    "**2. Avec les relations précédentes, comment peut-on calculer la concentration à la membrane et le flux de perméation pour une différence de pression donnée ?**\n",
    "\n",
    "> L'analyse du transfert de matière a permis de relier la concentration à la membrane, $c_m$ aux conditions opératoires, Pe :\n",
    "$$c_m=c_b e^{Pe}$$\n",
    ">L'analyse du transfert de quantité de mouvement (mécanique des fluides) permet de traduire l'effet de la concentration, $c_m$, à la membrane (par le biais de la pression osmotique, $\\Pi(c_m)$) à travers la loi de Darcy modifiée :\n",
    "$$J=\\frac{\\Delta P-\\Pi(c_m)}{\\mu R_m}$$\n",
    ">On dispose donc d'un système de deux équations à deux inconnues. Si la pression trans-membranaire est fixée, les inconnus sont le flux de perméation et la concentration à la membrane. Si on connait le flux à travers la membrane, les inconnus sont la pression transmembranaire et la concentration à la membrane. Il n' y a pas de solution analytique pour ces équations car le système est non linéaire. Il est par contre possible de combiner les deux équations afin d'avoir une équation à une inconnue ici par exemple en fonction de $c_m$ :\n",
    "$$\\frac{D}{\\delta}ln(\\frac{c_m}{c_0})-\\frac{\\Delta P-10^{+5}\\frac{133.75c_m}{100-c_m}}{\\mu R_m}=0$$\n",
    "\n",
    "\n",
    "**3. Réaliser ce calcul pour des pressions de 2, 5 et 10 bars et pour des vitesses de 0.05 m/s et 0.1 m/s.**\n",
    "\n",
    ">Le code suivant permet de résoudre le système d'équations avec la séquence de calculs suivantes :\n",
    "1. définition de la function pout le calcul de la pression osmotique\n",
    "2. definition de la fonction à une inconnu à résoudre pour déterminer cm\n",
    "3. boucle de calcul de cm pour les différentes valeurs de couche limite et de pression (deux boucles imbriquées pour balayer toutes les combinaisons de valeurs). Les valeurs de cm et J sont stockées dans un tableau.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
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