{ "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": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1190.4761904761906\n", "L'épaisseur de couche limite est de 256.7 micromètres pour une vitesse tangentielle de 0.05 m/s\n", "2.7270148074714534e-06\n", "L'épaisseur de couche limite est de 204.2 micromètres pour une vitesse tangentielle de 0.1 m/s\n", "3.427894085510686e-06\n", "\n", " J \\ u | 0.05 0.1\n", "------------------------------------------------------------------------------\n", " | Pe= 0.367 0.292\n", " 1.00e-06 | \n", " | cm= 0.289 0.268\n", "------------------------------------------------------------------------------\n", " | Pe= 0.733 0.583\n", " 2.00e-06 | \n", " | cm= 0.416 0.358\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "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=1200 #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=[1.e-6,2.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", "print (Sc)\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", " print (D/deltal[i])\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=1 um/s') \n", "plt.plot(x1,c_1, label='u=0.1 m/s J=1 um/s')\n", "plt.plot(x0,c_2, label='u=0.05 m/s J=2 um/s')\n", "plt.plot(x1,c_3, label='u=0.1 m/s J=2 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": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "u(m/s) delta(m) PTM(Pa) cm(%) J(m/s) \n", "0.05 2.57e-04 0.0 0.183 -2.45e-07\n", "0.05 2.57e-04 200000.0 0.35 1.53e-06\n", "0.05 2.57e-04 400000.0 0.634 3.15e-06\n", "0.05 2.57e-04 600000.0 1.065 4.56e-06\n", "0.05 2.57e-04 800000.0 1.651 5.76e-06\n", "0.05 2.57e-04 1000000.0 2.374 6.75e-06\n", "0.05 2.57e-04 1200000.0 3.208 7.57e-06\n", "0.05 2.57e-04 1400000.0 4.121 8.25e-06\n", "0.05 2.57e-04 1600000.0 5.09 8.83e-06\n", "0.05 2.57e-04 1800000.0 6.095 9.32e-06\n", "0.05 2.57e-04 2000000.0 7.123 9.74e-06\n", "0.1 2.04e-04 0.0 0.186 -2.49e-07\n", "0.1 2.04e-04 200000.0 0.317 1.58e-06\n", "0.1 2.04e-04 400000.0 0.523 3.30e-06\n", "0.1 2.04e-04 600000.0 0.83 4.88e-06\n", "0.1 2.04e-04 800000.0 1.256 6.30e-06\n", "0.1 2.04e-04 1000000.0 1.805 7.54e-06\n", "0.1 2.04e-04 1200000.0 2.469 8.61e-06\n", "0.1 2.04e-04 1400000.0 3.23 9.54e-06\n", "0.1 2.04e-04 1600000.0 4.069 1.03e-05\n", "0.1 2.04e-04 1800000.0 4.966 1.10e-05\n", "0.1 2.04e-04 2000000.0 5.906 1.16e-05\n" ] } ], "source": [ "Rm=1e14\n", "#Fonction pour le calcul de la pression osmotique en Pa\n", "def PI(c):\n", " PI=1.e5*(133.75*c/(100.-c))\n", " return PI\n", "#Foncion à résoudre pour déterminer la concentration à la membrane\n", "def f(cm):\n", " f=(D/delta)*np.log(cm/c0)-(DP-PI(cm))/(mu*Rm)\n", " return f\n", "#creation des tableaux de valeurs\n", "DPl=np.linspace(0,20.e5,21)\n", "cm=np.zeros(len(deltal)*len(DPl))\n", "J=np.zeros(len(deltal)*len(DPl))\n", "print ('u(m/s) delta(m) PTM(Pa) cm(%) J(m/s) ')\n", "for i in range(len(deltal)):\n", " for j in range(len(DPl)):\n", " delta=deltal[i]\n", " DP=DPl[j]\n", " cm[j+len(DPl)*i]=newton(f,c0)\n", " J[j+len(DPl)*i]=(D/delta)*np.log(cm[j+len(DPl)*i]/c0) \n", " if j%2 ==0:\n", " print (u[i],' ', \"%.2e\"%delta,' ', DP,' ',round(cm[j+len(DPl)*i],3),' ', \"%.2e\"%J[j+len(DPl)*i]) \n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**4. Tracer le flux de perméation en fonction de la différence de pression pour les deux vitesses et conclure.**" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "#Tracé de la concentration à la membrane\n", "plt.plot(DPl/1e5,cm[:j+1], label='u=0.05 m/s') \n", "plt.plot(DPl/1e5,cm[j+1:], label='u=0.1 m/s') \n", "plt.legend(loc='upper center')\n", "#plt.title('Evolution de la concentration au voisinage de la membrane en fonction de pression trans-membranaire')\n", "plt.xlabel('Pression trans-membranaire (bar)')\n", "plt.ylabel('Concentration du jus de fruit à la membrane (%)')\n", "plt.show() \n", " \n", "#Tracé du flux de perméation\n", "plt.plot(DPl/1e5,J[:j+1], label='u=0.05 m/s') \n", "plt.plot(DPl/1e5,J[j+1:], label='u=0.1 m/s')\n", "plt.plot(DPl/1e5,DPl/(mu*Rm), 'r--', label='eau pure')\n", "plt.legend(loc='upper center')\n", "#plt.title('Evolution du flux de perméation en fonction de pression trans-membranaire')\n", "plt.xlabel('Pression trans-membranaire (bar)')\n", "plt.ylabel('Flux de perméation (m/s)')\n", "plt.show() " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ ">On note que l'**augmentation de la pression** conduit toujours à une augmentation du flux de perméation. Toutefois, cette augmentation devient moins importante pour les hautes pressions car l'augmentation de la concentration à la membrane engendre une contre pression osmotique qui limite la perméation. On peut aussi noter pour les pressions inférieures à la pression osmotique de la dispersion que les flux de perméation sont négatifs : c'est un régime d'osmose et le flux de perméation est dirigé vers les hautes concentrations (c'est à dire du perméat vers le concentrat). Pour les pressions plus élevées, on force le fluide à aller du concentrat vers le filtrat : c'est le régime d'osmose-inverse. Ce type de calcul peut ainsi servir à calculer des unités de dessalement d'eau de mer par osmose inverse : il vous suffit de modifier les propriétés de la membrane, $R_m$ et la variation de la pression osmotique, $\\Pi$ en fonction de la concentration (la pression osmotique des sels sera beaucoup élevée: l'eau de mer à une pression osmotique de 25 bars). Il faudra donc également examiner des gammes de pression plus élévées (>25 bars) pour décrire l'osmose inverse. \n", ">\n", "> On note que l'**augmentation de la vitesse tangentielle** conduit à réduire la concentration à la membrane (effet du balayage tangentiel qui réduit l'épaisseur de la couche limite) et ainsi permet d'augmenter le flux de perméation (la contre pression osmotique est moindre)." ] }, { "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": "3.7.3" } }, "nbformat": 4, "nbformat_minor": 2 }