{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Liquid/liquid equilibrium : ternary diagram and extraction\n", "\n", "The code allow to create the ternary diagram (in weight %) for the isopropyl ether (diluant D), acetic acid (solute A) and water (solvent S). It plots the binodal curve and the tie lines (conodales in French). It allows to give the answers to the following questions :\n", "\n", "One want to realize the extraction of the acid from a solution of 4 kg of isopropyl ether and 1 kg of acetic acid with 3 kg of water. \n", "a) Determine from the equilibrium the partition coefficient (with a linear regression of the mass ratio in the concentration range used during the extraction)\n", "\n", "It is then possible to calculate the extraction for a given mixture i.e. the composition and the weight of the extract and the rafinate phases. " ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "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", "#S for solvent, A for solute and D for diluant\n", "#SP for solvent phase DP for diluant phase\n", "# Equilibrium data \n", "xA_SP=np.array([0.69, 1.41,2.89,6.42,13.3,25.5,36.7,44.3,46.4])\n", "xS_SP=np.array([98.1 , 97.1,95.5,91.7,84.4,71.1,58.9,45.1,37.1])\n", "xA_DP=np.array([0.18, 0.37,0.79,1.93,4.82,11.4,21.6,31.1,36.2])\n", "xS_DP=np.array([0.5,0.7,0.8,1,1.9,3.9,6.9,10.8,15.1])\n", "\n", "#functions to change the coordinate from x,y plot to a ternary diagram\n", "def tri(xA,xS):\n", " X=xS+xA/2\n", " Y=xA*np.sqrt(3)/2\n", " return X,Y\n", "def detri(X,Y):\n", " xA=Y*2/np.sqrt(3)\n", " xS=X-xA/2\n", " return xA,xS\n", "#calcul of the position of data point in the x,y plot\n", "XSP,YSP=tri(xA_SP,xS_SP)\n", "XDP,YDP=tri(xA_DP,xS_DP)\n", "#plot of ternary diagram\n", "def ter_diag():\n", " #Coordinates of based line\n", " xA_line=np.array([100, 0,0,100])\n", " xS_line=np.array([0,100,0,0])\n", " #Coordinates of intermediate line\n", " xA_uline=np.array([80, 80, 0,20,20, 0,80,60,60,0,40,40,0,60])\n", " xS_uline=np.array([0, 20,20,0 ,80,80, 0,0,40,40,0,60,60,0])\n", " #plot\n", " bbox_props = dict(boxstyle=\"round,pad=0.3\", fc=\"white\", ec=\"white\", lw=1)\n", " fig, ax = plt.subplots(figsize = (12, 12)) \n", " plt.plot(XSP,YSP,color='green', marker='o', linestyle='dashed')\n", " plt.plot(XDP,YDP,color='red', marker='o', linestyle='dashed')\n", " X,Y=tri(xA_uline,xS_uline)\n", " plt.plot(X,Y,'--', color='silver')\n", " X,Y=tri(xA_line,xS_line)\n", " plt.plot(X,Y)\n", " for i in range(len(xA_SP)):\n", " X=np.array([XSP[i],XDP[i]])\n", " Y=np.array([YSP[i],YDP[i]])\n", " plt.plot(X,Y, color='grey')\n", " ax.axis(\"off\")\n", " plt.text(-5, 0, \"D\", ha=\"center\", va=\"center\", size=20, bbox=bbox_props)\n", " plt.text(105, 0, \"S\", ha=\"center\", va=\"center\", size=20, bbox=bbox_props)\n", " plt.text(50, 90, \"A\", ha=\"center\", va=\"center\", size=20, bbox=bbox_props)\n", " return\n", "\n", "ter_diag()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### a) Determination of the partition coefficient\n", "\n", "The determination of the partition coefficient is based on the assumption of \n", "- non miscible solvent (Assumption 1) : there is no ether in aqueous phase and no water in ether phase\n", "- the distribution curve Y=f(X) is linear\n", "\n", "The distribution curve is not really lienar on the whole concentration range. The linear regression is then done on the concentration range that will be used in the experiments (i.e. a mass ratio X less than 0.25). There is 9 points on the distribution curve only the 5 first are used for the regression.\n" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[0.00181232 0.00374002 0.00802764 0.01988256 0.05167238 0.13459268\n", " 0.3020979 0.53528399 0.74332649] [0.00703364 0.01452111 0.03026178 0.07001091 0.15758294 0.35864979\n", " 0.62308998 0.98226164 1.25067385]\n" ] }, { "data": { "image/png": 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KlCZ1ajDklOYM6hrLOR1jqF0j/P46Dr+KjDFlU1wMzz3nFvCpXh2efhpq1/a7KoO7n7Aiu4CZ6Tl8kZ5D+sYCANo3rcN157ZjUJdYerZuRHRUeD+1bgFhTCTasgWGDnXtMoYPh1decWs3GN/sKypmwdqtfBG4n7Axfy8ikNimEQ8M7czArrEkNI2s5VktIIyJRI0aQdu2cOed8PvfW/8kn+TvLmT26lxmpecw54fN7NxXxEnVozm3Ywx3DjqZAZ2b0aRuTb/LPG4WEMZEiu+/h7vugvfec1cL//qX3xVVSRu27j44dPT9T1spLlFi6tZkePcWDOwSy9kdYqhVvXJMDrCAMCbc7d4NDz8Mzz4LLVrAhg02nFSBSkqUpVn5B28yr87ZAcDJsXW54bz2DOoaS/f4hkSF+f2E42EBYUw4mz3brQW9dq1b9nPsWGuuVwH2FhbzbcYWZqbn8OXKHHJ37CNK4Iy2jfnrhV0Y1DWWNk0qf7sSCwhjwtkbb7i1Gr7+2q3dYDyzddd+vlqVy6z0Tcz7MY/d+4upUyOa8zs1ZWCXWPp3akajOjX8LrNCWUAYE25mzIB27dwT0Aea69n0VU+sy9vFrPRNfJGeS8rPWylRiK1fk0t6xjGoayxnJTShZrXKcT/heFhAGBMucnPhz392fZQONNez4aRyVVyiLN6wjVnp7kohY/MuADo3r0dS/w4M7BrLaXENPG1tEUksIIzxmypMmQK33QY7dsDjj7sV30y52LO/mP+syWNW+ia+WpVL3s79VIsSzmzfmCv7tGFgl1haNbYrtFAsIIzx25tvwh//6JYAff116NrV74oi3uYd+/hqVQ6z0nP5z5rN7C0soV7NavTr3IyBXZrRr1MzGpxU3e8yw54FhDF+KCmBzExo3do96FZU5ELCmusdF1UlY/POg0NHaRu2owpxDU/i94mtGNS1Ob3bNaZGtSi/S40oFhDGVLQff/yluV56umuud911flcVcYqKS0hdv93dZF6Zy7o8dz/h1Lj63H7ByQzs2oyuLerb/YQTYAFhTEUpKnIPuz38MNSsCc88Y7OTjtGufUXM+3EzM9NzmL0ql227C6keLZyVEMO1Z7flgi6xtGx4kt9lVhqlBoSIfALcrKo/VVw5xlRSeXmuuV5KClx8Mbz0ErRs6XdVESGnwC29+UV6Dt9kbGF/UQn1a1VjQOdmDOranPNOjqFeLbuf4IUjXUFMBmaKyD+A/1XVwmN5YxGZBFwE5KrqqSH2C/A8MAzYDfxRVVMD+4YE9kUDE1V17LF8tjFhp3FjSEhws5MuvdSa6x2BqrI6Z8fB1hZLAktvtmp8Elee2YaBXZtxRtvGVI+2+wleKzUgVPVfIvIx8DCQIiJvASVB+585yntPBsYBb5ayfyjQMfB1JvAKcKaIRAMvAYOATGChiMxQ1fQy/RcZEy6+/dY113v/fdc76b33/K4obBUWl7Dwp1+W3tywdQ8A3Vs15O7BJzOoa3NOjvV26U1zuKPdgygEdgE1gXoEBcTRqOpcEWl7hENGAG+qW/N0gYg0FJEWQFtgjaquBRCR9wLHWkCYyLBrF/zlL/DCC24J0KysKt9cb/ycDLrFN6BvQszBbV+uzGHGkmwE+GpVLgV7i6hRLYqzE5pw0/kduKBLM2LrV9zSm+ZwR7oHMQR4BpgB9FLV3eX82XHAhqDXmYFtobafeYQ6xwBjAFq3bl3OJRpzjL74ws1Q+uknuOUW+O//hnr1/K7Kd93iG5A0JY3HRpzCtl37+VfKBpZluVXWGtWuzqCuzRnUtRnndmxKnZo2dyZcHOl34i/Af6nqCo8+O9S1oh5he0iqOgGYAJCYmFjqccZUiLffhho1YO5cOPdcv6sJCzv3FZG1bQ/N69ciaUoaAFECF57WnKv7tqNX64ZUs/sJYelI9yC8/r87E2gV9DoeyAZqlLLdmPA0fTq0bw/durlhperV4aSqPdWyqLiEbzK2kJyayecrNrG3sITWjWtzZrvGfLduK7f078Bdgzv5XaY5Cj+v5WYASYF7DGcC+aq6UUQ2Ax1FpB2QBVwGjPaxTmNCy8mBW291N6GvvhomT4b69f2uylcrNxaQnJrJ9MXZbN6xj/q1qjGyVzyjesWxr7CEpHfT+POADrz93XrOSmjyq3sSJvx4FhAi8i7QD4gRkUzgEaA6gKqOBz7BTXFdg5vmek1gX5GIJAGf46a5TvJwmMuYY6fqhpJuvx127oQnn4R77vG7Kt/kFuzlw8XZJKdlsXJjAdWihH6dmjGqVxz9OzejVvVo5mfkkfRuGuNG96RvQgx9EpqQNOWX1yY8iZtEVDkkJiZqSkqK32WYyu4f/3B9k/r2dc31Onf2u6IKt2d/MTPTN5GcmsW8HzdTotA9vgEje8VzUbcWNKlb81fHh5rFND8jj6WZ+dx4fkJFl2+CiMgiVU0Muc8CwpgyKClxa0G3aQP79rn23FddVaWa65WUKN+t20pyaiafLt/Ezn1FtGxQi0t6xXFJz3g6NKvrd4nmOBwpIGw+mTFHs3q1Wxf6559dc726deGaa/yuqsKsyd3JtLRMpqdlk7V9D3VqRDPstBaM7BXPme0aExVlD69VVhYQxpSmsBCefhoefdQ11Xv2Wdd5tQrYums/Hy3JJjk1kyWZ+UQJnNuxKfcO6cTgrs05qUbVuXKqyiwgjAklLw8GD4a0NBg1CsaNg+bN/a7KU/uKivlqZS5TU7P4enUuRSVKlxb1+cuwLozo0ZJm9lRzlWMBYUwwVddIr0kT6NLFtcwYNcrvqjyjqqSu38bU1Cw+XrqR/D2FNK1Xk2vObsslPePp2rJqT9ut6iwgjDngm2/gzjth6lSIj4d33vG7Is+s37KbaWlZJKdl8vOW3dSqHsVvTmnOyF7xnJ3QxJ5sNoAFhDHuWYYHH3TDSK1bw8aNLiAqmfw9hXyybCPJqZks/GkbItCnXROS+ndgyKnNbU0FcxgLCFO1zZwJY8bA+vWQlAR//7ubpVRJFBaXMPeHzSSnZjFrZQ77i0pIaFqHe37TiYt7xhFnq6+ZI7CAMFXblCmub9K8eXD22X5XUy5UleVZBUxNzeSjJdls2bWfxnVqMLp3a0b2iuO0uAa2roIpEwsIU/VMnQodOkD37q65Xo0aUCvyZ+hkb9/D9MVZTEvN4sfcndSIjmJg12Zc0jOe809uSo1qdl/BHBsLCFN1bNrk1mhITnatMt54I+Kb6+3cV8RnyzcxLS2T+RlbUIXENo148pJTuei0ljSobfcVzPGzgDCVn6rrn3THHbBnj1vE5+67/a7quBWXKPMz8khOzeKz5ZvYU1hM68a1+fOAjlzSM462MVXjYT7jPQsIU/lNngzXXusW8HntNegUmesQrNpUwLTULKYvziKnwLXSvrhnHKN6xXF6m0Z2X8GUOwsIUzkVF7vmem3bwujRrqnelVdCVGSNw+fu2MuMxdkkp2aRfrCVdlMeGR7PgEArbWO8YgFhKp+VK11zvQ0b3Pd16rjOqxFib2ExM9NzSE7NZN6PeRSXKN3iG/Do8K4M797ysFbaxnjF04AQkSHA87iFfyaq6thD9t8DXBFUSxegqapuFZGfgB1AMVBUWjtaYw4qLIT//V947DH3LMNzz7kmexGgpET5/qdAK+1lm9ixr4gWDWpxw3ntGdkrjg7N6vldoqmCvFxRLhp4CRiEW396oYjMUNX0A8eo6lPAU4HjhwN3qOrWoLfpr6p5XtVoKpHNm2HQIFiyBH73Ozd9NTbW76qOKmPzTqalZjEtLetgK+2hp7VgZM84+rRvYq20ja+8vILoDaxR1bUAgbWnRwDppRx/OfCuh/WYyuhAc72YGDjtNNea++KL/a7qiLbt2s+/l2YzNTWLxRu2EyVwTsem3PObTgw+JZbaNWzk14QHL/9PjAM2BL3OBM4MdaCI1AaGAElBmxWYKSIKvKqqE0o5dwwwBqB169blULaJGHPnwl13wbRprnfSW2/5XVGp9hUVM3vVZpJTM5m9OpfCYqVz83o8OKwzI3rEEWuttE0Y8jIgQl0bl7a+6XDgm0OGl85W1WwRaQbMEpFVqjr3sDd0wTEB3JKjJ1q0iQAFBfDAA/Dyy9CunXsALgyb66kqaRu2k5yayUdLfmmlffVZbRnZy1ppm/DnZUBkAq2CXscD2aUcexmHDC+panbg11wRmYYbsjosIEwV8+mncMMNkJkJt98OTzwRdqu8bdjqWmlPS8tiXd4ualWPYnDX5ozsFcc5HWKslbaJGF4GxEKgo4i0A7JwITD60INEpAFwPnBl0LY6QJSq7gh8Pxh4zMNaTaR4/32oVw/mz4c+ffyu5qCCvYV8snQjyWlZfL/OXQj3ad+Ym/olMNRaaZsI5VlAqGqRiCQBn+OmuU5S1RUicmNg//jAoZcAM1V1V9DpscC0wJOh1YApqvqZV7WaMKbqQuHkk6FHD3j+eddcr6b/zwIUFpcw78dAK+30HPYVldA+0Ep7RI+WxDeKjCm2xpRGVCvPsH1iYqKmpKT4XYYpL9nZrrne9OlwzTUwaZLfFaGqrMguIDk1ixlLssjbuZ9Gtavz2+4tGdkrnm7x1krbRBYRWVTac2Y2n86EH1UXBnfdBfv2wVNPufsNPtqUv5fpi7NITs3khxzXSvuCLs24pGcc/To1s1baplKygDDhZ/Jk1yrj/PNh4kS3doMPdu0r4vMVm0hOzeKbjDxU4fQ2jXji4lO5qFsLGtau4UtdxlQUCwgTHoqL4eefoX1711yvenX3awU31ysuUb7N2EJyaiafrdjE7v3FtGp8ErcGWmm3s1bapgqxgDD+W7ECrrsOsrJg1So3bfXKK49+Xjn6IWcHU1Mz+TAtm00Fe6lXqxojerj7ConWSttUURYQxj/798PYse5Zhvr1Xf8kj5rrjZ+TQbf4BvRNiDm47dNlG/lgUSY5O/ayPKuA6Cih38lNeeiirlzQxVppG2MBYfyxeTNccAEsWwaXX+6mrzZt6tnHdYtvQNKUNJ75XXd27ivi9XnrSNuwHYDT4hrwSKCVdoy10jbmIAsIU7GCm+v17AlPPgnDh3v8kUqt6tH0bNWQa95YiAJRAr/t3pJbB3SgY6y10jYmFAsIU3G+/tpNXZ0+HVq1cutEe2hT/l6S0zL5YFEmaze7lhedmtdj1aYd3NyvA3f/JjKXHjWmolhAGO/l58N998Grr7pZSrm5LiA8cGA1tg8WZfKfHzdTotC7bWNuPC+BJnVrcM8HS/nzgA68/d16+nZo8qt7EsaYX7OAMN76+GPXXG/jRnf18Nhj5X4j+kDX1A8WZfLRkmx27C0iruFJJPXvwMhe8bSNqcP8jDySpqQxbnRP+ibE0Cehya9eG2MOZwFhvDV1KjRqBMnJ0Lt3ub51qCGkYae24NLT4w9bjW1pZv6vwqBvQgzjRvdkaWa+BYQxpbBeTKZ8qcI//wmdOrmb0Dt2uMZ6NcrnqeO9hcXMCgwhzQsaQrr09HiGnmZdU405VtaLyVSMzEy4+Wb46CO49lp4/XXXmvsEqSqLA0NIMwJDSC0b1OKW/h0YFRhCMsaUPwsIc+JKSlzPpHvugcJCePppuO22E37bTfl7mZaWxQeLNpARGEIaGhhCOuuQISRjTPmzgDAnbvJkdyN6wACYMAESEo77rUINIZ3RthFjzmvPsNNa2BCSMRXI04AQkSHA87gFgyaq6thD9vcDPgTWBTYlq+pjZTnX+Ky4GNatc51Wr7zSzUz6/e/dQ3DHKHgI6aMl2RTYEJIxYcGzgBCRaOAlYBBufeqFIjJDVdMPOXSeql50nOcaPyxb5prrZWfD6tWuud5llx3z29gQkjHhzcsriN7AGlVdCyAi7wEjgLL8JX8i5xqv7NsHf/+7+2rUCF588ZifabAhJGMih5cBEQdsCHqdCZwZ4rizRGQJkA3craorjuFcU1Fyc909hhUr4Ior4LnnXD+lMjjSENLIXvG2xoIxYcrLgAg1PnDoQxepQBtV3Skiw4DpQMcynus+RGQMMAagdevWx12sKcWB5npNm8IZZ8D//A9ceGGZTs0p2Etyqg0hGROpvAyITCC44U487irhIFUtCPr+ExF5WURiynJu0HkTgAngHpQrn9INAF995dpjzJjheie98cZRT7EhJGMqDy8DYiHQUUTaAVnAZcDo4ANEpDmQo6oqIr2BKGALsP1o5xoPbd/unmk4sB50Xt4Rm+vZEJIxlZNnAaGqRSKSBHyOm6o6SVVXiMiNgf3jgUuBm0SkCNgDXKau90fIc72q1QSZMQNuugk2bYJ774VHH4WTTgp5aKghpCGnNOe/ElvZEJIxlYD1YjK/9qc/wcKFrk1G4uHtWUINISW2acSlp8czrFsL6tsQkjERxXoxmdKpwpQp0KUL9OrlZifVqPGr5nqqypLMfD5YtIEZi90QUosGtbi5XwdGnW5DSMZUVhYQVdmGDXDjjfDJJ+7Bt4kToW7dg7tzCg48yJbJmtyd1KwWxdBTm3Pp6a04K6EJ0TaEZEylZgFRFZWUuNXd7rvPtcx47jlISgLcENIXK90Q0twffhlCGjvyNBtCMqaKsYCoiiZPdm25Bw6ECRPQtm1tCMkYcxgLiKqiqMg11+vY0TXXq1uXnN8MZ9ribD6YNteGkIwxh7GAqITGz8mgW3yDX5bSXLKEnVdeDZs2Ue3HH/hi/U4+2NWWuWO/siEkY0ypLCAqoW7xDUiaksZLo7py1rvjKRk7ln016/Kvq+/llWfnU7Cv+OAQ0shecbRvWvfob2qMqXIsICqhvgkxvPqbeJr06wub1zPt1AE8PuBP7KnXkKFdYm0IyRhTJhYQlY0qRSXKqqJa1GrZmb/1u44fep7NfRd05EIbQjLGHAMLiMpk1ix23Xo7N/zuUf6zvzbVht3GpYnxLFuRQ5smtS0cjDHHJMrvAkw52LaNHVdcDYMHs2lzPrp1C3VrVuPNa3szdmQ3xo3uSdKUNOZn5PldqTEmgtgVRITb88/3Kb7pZk7avpUJZ/+ekoce4qzqNbilTaODs5j6JsQwbnRPlmbm/zKzyRhjjsICIkKVlCgfLMqkxlOT6Fi9PjP/+0WuuOlimtWvFfL4vgkxFg7GmGNiARFpVFn7zCu8kFOT6VHNOeuKu7h/RHfuaN/U78qMMZWMBUQE2bR0NVv/cA1dl35LvzOG0X/CBH7bvSUiNl3VGFP+7CZ1BNizt5Cvbn2Eemf0pM3KNL66+a8MnjuNET3iLByMMZ7xNCBEZIiIrBaRNSJyf4j9V4jI0sDXfBHpHrTvJxFZJiKLRaRKrgKkqny4OItnr3iAAeMeY/3J3ShYmMqAlx6ndq0aR38DY4w5AZ4NMYlINPASMAjIBBaKyAxVTQ86bB1wvqpuE5GhwATgzKD9/VW1Ss7NXLpuMxP+8SX/3luPHucM48cBp9Dl5j+CXTEYYyqIl/cgegNrVHUtgIi8B4wADgaEqs4POn4BEO9hPREht2Avb4//kMHP/IWHd2+n/7+/4eJzTra2GMaYCudlQMQBG4JeZ/Lrq4NDXQd8GvRagZkiosCrqjoh1EkiMgYYA9C6desTKthPewuL+cfsVchjj/Pn+e+zt2Ejoie8zKjzOvldmjGmivIyIEL9k1dDHijSHxcQ5wRtPltVs0WkGTBLRFap6tzD3tAFxwSAxMTEkO8fzlSVz1fk8PK/5vPsS7eRsDWTHZf/gXovPQ+NGvldnjGmCvMyIDKBVkGv44HsQw8SkW7ARGCoqm45sF1VswO/5orINNyQ1WEBEclWbSrgsRkrmL92Kyc3a0ydgf3huiupN3iw36UZY4ynAbEQ6Cgi7YAs4DJgdPABItIaSAb+oKo/BG2vA0Sp6o7A94OBxzystUJt3bWfZ2atZsO70/jb12+w9JW3GDGiL9Wi+/ldmjHGHORZQKhqkYgkAZ8D0cAkVV0hIjcG9o8HHgaaAC8H5vMXqWoiEAtMC2yrBkxR1c+8qrWiFBaX8Na3PzPpo0Xc8el4nlj2JcWdOtExoR5E2yMpxpjwIqoRN2xfqsTERE1JCc9HJr5encvj/06n439mMvarV2mwKx+5/37461+hVuj+ScYY4zURWRT4h/lhrNVGOTpsLWjgg0UbeHl2BmvzdtEupg4PVd9Ag4Q2yKRJ0KOHf8UaY8xRWECUowNrQY8b3ZNTWjbg/qlL+XTZRkanf8mtw8/nwmvPo8a+M6BmTahmP3pjTHizv6XKUd+EGMZd3pPr/5FCsSoxeRv597xXOXXF99ByN4y5GKrV8btMY4wpEwuIcpS1fQ/j565lz979XJX6MQ988xY1q0XDyy/DDTf4XZ4xxhwTC4hyUFKivPP9esZ+spKiEmX0ytk8+uUE/tPxDGq9PoHEc3v4XaIxxhwzm1t5gn7K28Xlry3gb1MXc25xHrWqR3PhU/dCcjJRn3zMmK8321rQxpiIZFcQx6m4RHnjm3X838zVdMvNYOHsV6ixNY9ls7+nT+cW0PkS+oKtBW2MiVgWEMfhx5wd3PPBUlauzeG5VR8y5PN3kGbNYOKr9Dmtza+OtbWgjTGRygLiGBQWl/DqnAxe+HINrQoLWPTBA9Rdvw6uuw7+7/+gYUO/SzTGmHJjAVGKQx96W56Vzy3vpLJ+y04u7B7Ho8P7Uzf/K/jd7+CCC3yu1hhjyp8FRCkOPPT27O+7s3DdNl7+eg3nZyxk2ndv0/imL6BeLXj1Vb/LNMYYz1hAlKJvQgyP/vYUrp2cQv2d23l29kRGLJ8NXbtCQYHf5RljjOdsmituOOnQqagT563lvg+WcuHKecx6/WYuWjkPHn4YUlOhWzefKjXGmIpjAcEvw0nzM/JQVR6avpwnPl5J7RpRnLdhKUXxrbj8xpeYf9Wtro+SMcZUAVU+IMbPyQDc8wq3vJPKkGfnsO/V1zhv+1pKFOInv0LzFWncfsfIgyFijDFVgacBISJDRGS1iKwRkftD7BcReSGwf6mI9CrrueVh/JwMoqMgaUoaBXsKaVuQw8Mv3Mb/fvYCN6+dy0tX9KLPqa2hWjXXiC/w0JsxxlQFnt2kFpFo4CVgEG596oUiMkNV04MOGwp0DHydCbwCnFnGc0/YgaGly3u1ZOFtDzNl7lsURUXx6LBbGfzcXw97wM0eejPGVCVeXkH0Btao6lpV3Q+8B4w45JgRwJvqLAAaikiLMp57wvomxDB25GnkjXuVh76ayPw23Xj62WkMfuFhkt5bYsNJxpgqzctprnHAhqDXmbirhKMdE1fGcwEQkTHAGIDWrVsfc5GDT2nOo2cN4/raDcgfOIQ1ebsZjPVQMsYYL68gJMS2QxfALu2YspzrNqpOUNVEVU1s2rTpMZYIr83LYOPuYur+biRr8nZzU7/2JE1JA+DG8xOO+f2MMaay8PIKIhNoFfQ6Hsgu4zE1ynDuCZufkcczM3/kwQs7c/25CczPyCNpSho39WtvVw/GmCrPyyuIhUBHEWknIjWAy4AZhxwzA7gqMJupD5CvqhvLeO4JW5qZz+t/TOT6c92VwoGZSsUldvVgjDGeXUGoapGIJAGfA9HAJFVdISI3BvaPBz4BhgFrgN3ANUc6t7xrDBUCNlPJGGMcUQ05tB+REhMTNSUlxe8yjDEmYojIIlVNDLWvyj9JbYwxJjQLCGOMMSFZQBhjjAnJAsIYY0xIleomtYhsBn4+jlNjgHDvq2E1lg+rsXxYjeUjHGpso6ohnzKuVAFxvEQkpbS7+OHCaiwfVmP5sBrLR7jXaENMxhhjQrKAMMYYE5IFhDPB7wLKwGosH1Zj+bAay0dY12j3IIwxxoRkVxDGGGNCsoAwxhgTUpUKCBEZIiKrRWSNiNwfYr+IyAuB/UtFpFcY1thZRL4VkX0icndF11fGGq8I/PyWish8EekehjWOCNS3WERSROSccKsx6LgzRKRYRC6tyPoCn320n2M/EckP/BwXi8jD4VZjUJ2LRWSFiMwJtxpF5J6gn+HywO9344qu8zCqWiW+cG3DM4D2uAWJlgBdDzlmGPApbkW7PsB3YVhjM+AM4Eng7jD9OfYFGgW+HxqmP8e6/HIPrhuwKtxqDDruK1xr/EvDrUagH/Dviv7/8BhrbAikA60Dr5uFW42HHD8c+Mqvn2nwV1W6gugNrFHVtaq6H3gPGHHIMSOAN9VZADQUkRbhVKOq5qrqQqCwAusKVpYa56vqtsDLBbgVAcOtxp0a+NMI1KGUJW39rDHgVmAqkFuRxQWUtUY/laXG0UCyqq4H92coDGsMdjnwboVUdhRVKSDigA1BrzMD2471GC/5/fllcaw1Xoe7KqtIZapRRC4RkVXAx8C1FVTbAUetUUTigEuA8RVYV7Cy/l6fJSJLRORTETmlYko7qCw1ngw0EpGvRWSRiFxVYdU5Zf4zIyK1gSG4fxT4zss1qcONhNh26L8ay3KMl/z+/LIoc40i0h8XEBU9vl+mGlV1GjBNRM4DHgcGel1YkLLU+Bxwn6oWi4Q63HNlqTEV18tnp4gMA6YDHb0uLEhZaqwGnA5cAJwEfCsiC1T1B6+LCziWP9fDgW9UdauH9ZRZVQqITKBV0Ot4IPs4jvGS359fFmWqUUS6AROBoaq6pYJqO+CYfo6qOldEEkQkRlUrqnFaWWpMBN4LhEMMMExEilR1eoVUWIYaVbUg6PtPROTlMPw5ZgJ5qroL2CUic4HuQEUFxLH8/3gZYTK8BFSpm9TVgLVAO365UXTKIcdcyK9vUn8fbjUGHfso/tykLsvPsTVunfG+Yfx73YFfblL3ArIOvA6XGg85fjIVf5O6LD/H5kE/x97A+nD7OQJdgC8Dx9YGlgOnhlONgeMaAFuBOhX5+3ykrypzBaGqRSKSBHyOm1UwSVVXiMiNgf3jcTNFhuH+ctsNXBNuNYpIcyAFqA+UiMjtuBkRBaW9b0XXCDwMNAFeDvzrt0grsGNlGWscBVwlIoXAHuD3GvhTGkY1+qqMNV4K3CQiRbif42Xh9nNU1ZUi8hmwFCgBJqrq8nCqMXDoJcBMdVc6YcFabRhjjAmpKs1iMsYYcwwsIIwxxoRkAWGMMSYkCwhjjDEhWUAYY4wJyQLCGI+ISCsRWXegK6eINAq8buN3bcaUhQWEMR5R1Q3AK8DYwKaxwARV/dm/qowpO3sOwhgPiUh1YBEwCbge6Kmuo6cxYa/KPEltjB9UtVBE7gE+AwZbOJhIYkNMxnhvKLARONXvQow5FhYQxnhIRHoAg3DNH++o4AWojDkhFhDGeERcp8JXgNvVrWb2FPB//lZlTNlZQBjjneuB9ao6K/D6ZaCziJzvY03GlJnNYjLGGBOSXUEYY4wJyQLCGGNMSBYQxhhjQrKAMMYYE5IFhDHGmJAsIIwxxoRkAWGMMSak/weMiu8begSYbAAAAABJRU5ErkJggg==\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "The partition coefficient for the whole concentration range is, K= 2.7333084919200994\n" ] } ], "source": [ "#calculation of mass ratio\n", "Y=xA_SP/xS_SP\n", "X=xA_DP/(100-xS_DP-xA_DP)\n", "#plot the distribution curve\n", "print(X, Y)\n", "plt.plot(X,Y, marker='x')\n", "plt.xlabel('X')\n", "plt.ylabel('Y')\n", "\n", "#regression lineaire \n", "def fit(x,m):\n", " return m*x\n", "from scipy.optimize import curve_fit\n", "m,p=curve_fit(fit, X[:6], Y[:6])\n", "K=m[0]\n", "plt.plot(X, fit (X,K), 'r--')\n", "plt.show()\n", "print ('The partition coefficient for the whole concentration range is, K=', K)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## b) Calcul des courants croisés 1 puis 3 étages avec le coefficient de partage" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "#Calculation for one stage\n", "m_A=1\n", "m_D=4\n", "m_S=3\n", "X0=m_A/m_D\n", "A=m_D\n", "S=m_S\n", "\n", "#Calculation of the Y1 and X1\n", "X11=(A/(A+(K*S)))*X0\n", "Y11=K*X11\n", "eff=(X0-X11)/X0\n", "\n", "#Fonction pour tracer les étages (cercle, flèche, resultats)\n", "def etage(xc,yc,rc,label,X1,Y1,S):\n", " circ=plt.Circle(( xc , yc ), rc )\n", " hl=0.1\n", " la=0.5-rc-hl\n", " plt.text(xc-0.1,yc-0.1,label, size=70)\n", " plt.arrow(xc-0.5,yc,la,0.,head_width=0.05, head_length=hl)\n", " plt.arrow(xc+rc,yc,la,0.,head_width=0.05, head_length=hl)\n", " plt.arrow(xc,1,0.,-la,head_width=0.05, head_length=hl)\n", " plt.arrow(xc,0.3,0.,-la,head_width=0.05, head_length=hl)\n", " plt.text(xc+rc,0.4,'A='+str(A), size=15)\n", " plt.text(xc+rc,0.3,'X'+label+'='+str(round(X1,3)), size=15)\n", " plt.text(xc+0.05,0.9,'S='+str(S), size=15)\n", " plt.text(xc+0.05,0.2,'S='+str(S), size=15)\n", " plt.text(xc+0.05,0.1,'Y1='+str(round(Y1,3)), size=15)\n", " ax.add_patch(circ)\n", "\n", "#Tracé du flowsheet pour 1 étage\n", "fig, ax = plt.subplots(figsize=(4, 4))\n", "etage(0.5,0.5,0.2,'1',X11,Y11,S)\n", "plt.text(0,0.4,'A='+str(A), size=15)\n", "plt.text(0,0.3,'X0='+str(X0), size=15)\n", "plt.text(0.8,0.8,'Eff='+str(round(eff,3)), size=15, c='r')\n", "ax.set_aspect( 1 )\n", "plt.axis('off')\n", "plt.show()\n", "\n", "#Calculation for 3 stages with S/3\n", "S=1\n", "coeff=(A/(A+(K*S)))\n", "X1=coeff*X0\n", "Y1=K*X1\n", "X2=coeff*X1\n", "Y2=K*X2\n", "X3=coeff*X2\n", "Y3=K*X3\n", "eff=(X0-X3)/X0\n", "\n", "#Tracé du flowsheet pour 3 étages\n", "fig, ax = plt.subplots(figsize=(12, 4))\n", "etage(0.5,0.5,0.2,'1',X1,Y1,S)\n", "etage(1.2,0.5,0.2,'2',X2,Y2,S)\n", "etage(1.9,0.5,0.2,'3',X3,Y3,S)\n", "plt.text(0,0.4,'A='+str(A), size=15)\n", "plt.text(0,0.3,'X0='+str(X0), size=15)\n", "plt.text(2.3,0.8,'Eff='+str(round(eff,3)), size=15, c='r')\n", "ax.set_xlim([0, 3])\n", "ax.set_aspect( 1 )\n", "plt.axis('off')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### d) Construction graphique (avec l'hypothèse d'un coeff de partition)\n", "\n", "La construction graphique permet de représenter les résultats d'une autre façon. Elle est très utilisée dans le cas où les calculs deviennent compliqués comme par exemple dans le cas des configurations à contre-courant que vous verrez en master." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(X,Y, marker='x')\n", "plt.plot(X,K*X,'r',label='Equilibrium line')\n", "plt.plot([X11,X0],[Y11,0],'b',label='Operating line for 1 stage')\n", "plt.plot([X3,X2,X2,X1,X1,X0],[Y3,0,Y2,0,Y1,0],'g',label='Operating lines for 3 stages')\n", "plt.xlim(0,0.3)\n", "plt.ylim(0,0.6)\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "e) Pour n étages avec la même quantité de solvant par étage, S, on peut démontrer que :\n", "\n", "$$\\frac{X_n}{X_0}=(\\frac{A}{A+KS})^n$$\n", "\n", "ou \n", "\n", "$$n=\\frac{ln(\\frac{X_n}{X_0})}{ln(\\frac{A}{A+KS})}$$\n", "\n", "\n", "f) Combien d’étages faudrait-il utiliser pour atteindre un rendement d’extraction de 85%, dans le cas où la quantité totale, $S_{tot} de solvant est toujours de 3 kg : chaque étage est alimenté par 3/n kg de solvent\n", "\n", ">Si on connaît le rendement d'extraction on peut déterminer la quantité présente dans le raffinat, Xn, en réalisant un bilan matière sur l'acide sur l'ensemble des n étages. La quantité totale extraite, $\\sum_{i=1}^{n} S_i Y_i$ est en effet égale à la quantité d'acide perdue dans le raffinat, $A(X_0-X_n)$.\n", ">\n", ">Le rendement d'extraction peut donc s'écrire en fonction de la quantité dans le raffinat au bout de n étages :\n", ">\n", ">$$\\eta=\\frac{\\sum_{i=1}^{n} S_i Y_i}{A X_n}=\\frac{A(X_0-X_n)}{A X_n}$$\n", ">\n", ">Soit : $X_n=X_0(1-\\eta)$\n", "\n", ">Pour connaître le nombre d'étage n, il faut résoudre l'équation suivante :\n", ">$$\\frac{X_n}{X_0}=(\\frac{A}{A+KS_{tot}/n})^n$$\n", ">Il faut donc passer par une méthode numérique pour résoudre cette équation et trouver n\n", "\n", "\n", "g) Combien de solvant faudrait-il utiliser pour atteindre un rendement d’extraction de 85% en conservant trois étages\n", "\n", "> Il faut résoudre l'équation suivante :\n", ">$$\\frac{X_n}{X_0}=(\\frac{A}{A+KS_{tot}/3})^3$$\n", ">soit:\n", ">$$S_{tot}/3=\\frac{A}{K}(\\frac{X_n}{X_0}^{(-1/3)}-1)$$\n", "\n" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "To reach an efficiency of 0.85 we need 12.4 cross current stages with 0.24 kg of solvent per stages\n", "To reach an efficiency of 0.85 we need 3.87 kg of solvent for the 3 stages : 1.29 kg of solvent per stages\n" ] } ], "source": [ "from scipy.optimize import newton\n", "\n", "eff=0.85\n", "Xn=X0*(1-eff)\n", "#function to solve to find n with 3/n kg of solvent per stage\n", "def f1(n):\n", " coeff=(A/(A+(K*3/n)))\n", " out=n*np.log(coeff)-np.log(Xn/X0)\n", " return out\n", "\n", "x=newton(f1, x0=1)\n", "print ('To reach an efficiency of ', eff, ' we need', round(x,2), 'cross current stages with',round(3/x,2), 'kg of solvent per stages')\n", "\n", "S=3*A/K*(((Xn/X0)**(-1/3))-1)\n", "print ('To reach an efficiency of ', eff, ' we need', round(S,2), 'kg of solvent for the 3 stages :',round(S/3,2), 'kg of solvent per stages')\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Calcul extraction 1 étage avec le diagramme ternaire\n", "Ce type de calcul est le plus précis et ne comporte pas d hypothèses majeures (en dehors du fait qu'on considère être à l'équilibre à la sortie d'un étage théorique) " ] }, { "cell_type": "code", "execution_count": null, "metadata": { "scrolled": true }, "outputs": [], "source": [ "m_A=1\n", "m_D=4\n", "m_S=3\n", "m_M=m_A+m_D+m_S\n", "XA_M=100*m_A/m_M\n", "XS_M=100*m_S/m_M\n", "#plot ternary diagram\n", "ter_diag()\n", "#plot the points and the line between the feed, the mixture 1 and the solvent\n", "X_F,Y_F=tri(100*m_A/(m_D+m_A),0)\n", "X_M,Y_M=tri(XA_M,XS_M)\n", "X_S,Y_S=tri(0.,100.)\n", "plt.scatter(X_F,Y_F, color='blue', marker='x')\n", "plt.plot([X_F,X_S],[Y_F,Y_S], color='blue', marker='x')\n", "\n", "#plot the mixture point\n", "X_M,Y_M=tri(XA_M,XS_M)\n", "plt.scatter(X_M,Y_M, color='red', marker='x')\n", "#find the two tie lines bordering the mixture \n", "c1=0\n", "c2=0\n", "for i in range(len(xA_SP)):\n", " if Y_M < YDP[i]+(YSP[i]-YDP[i])*(X_M-XDP[i])/(XSP[i]-XDP[i]):\n", " c1=i-1\n", " c2=i\n", " print ('There will be 2 phases and the mixure is located between the tie lines', c1,'and',c2)\n", " break\n", "if c2==0 : print ('There is only one phase : the separation is impossible')\n", "\n", "#determination of the tie line for the mixture \n", "\n", "#function to find the intersection point between two lines AB and CD\n", "def intersec(xA,yA,xB,yB,xC,yC,xD,yD):\n", " #slope of line A B\n", " AB=(yB-yA)/(xB-xA)\n", " #slope of line A B\n", " CD=(yD-yC)/(xD-xC)\n", " x=-(CD*xC-yC-AB*xA+yA)/(AB-CD)\n", " y=AB*(x-xA)+yA\n", " return x,y\n", "\n", "#find the intersection point I between the two bordering tie line\n", "X_I,Y_I=intersec(XDP[c1],YDP[c1],XSP[c1],YSP[c1],XDP[c2],YDP[c2],XSP[c2],YSP[c2])\n", "#find the intersection point between IM and the binodal curve (diluant side)\n", "X_DC,Y_DC=intersec(X_I,Y_I,X_M,Y_M,XDP[c2],YDP[c2],XDP[c1],YDP[c1])\n", "#find the intersection point between IM and the binodal curve (solvant side)\n", "X_SC,Y_SC=intersec(X_I,Y_I,X_M,Y_M,XSP[c2],YSP[c2],XSP[c1],YSP[c1])\n", "plt.scatter(X_DC,Y_DC, color='red', marker='x')\n", "plt.scatter(X_SC,Y_SC, color='red', marker='x')\n", "plt.plot([X_SC,X_DC],[Y_SC,Y_DC], color='red', marker='x')\n", "plt.show()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "### Calculation of the composition of the phases and their weight.\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "print ('The composition of the raffinate phase, R, is :')\n", "xA,xS=detri(X_DC,Y_DC)\n", "print ('x_A=', round(xA,2),'% x_S=', round(xS,2),'% x_D=', round(100-xS-xA,2),'%')\n", "print ('X_1=', round(xA/(100-xS-xA),2))\n", "print ('The composition of the extract phase, E, is :')\n", "yA,yS=detri(X_SC,Y_SC)\n", "print ('y_A=', round(yA,2),'% y_S=', round(yS,2),'% y_D=', round(100-yS-yA,2),'%')\n", "print ('Y_1=', round(yA/yS,2))\n", "m_E=m_M*(XA_M-xA)/(yA-xA)\n", "m_R=m_M-m_E\n", "print ('The mass of extract is :', round(m_E,2), 'kg and the mass of raffinate is : ', round(m_R,2), 'kg ')\n", "print(\"\")\n", "print('The efficiency is ', round(m_E*yA/m_A,2), '%')\n", "print('The efficiency is ', round(100*(m_A-m_R*xA/100)/m_A,2), '%')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Calcul extraction 3 étages avec le diagramme ternaire" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "m_A=1\n", "m_D=4\n", "m_S1=1\n", "m_S2=1\n", "m_S3=1\n", "m_M1=m_A+m_D+m_S1\n", "XA_M1=100*m_A/m_M1\n", "XS_M1=100*m_S1/m_M1\n", "#plot ternary diagram\n", "ter_diag()\n", "#plot the points and the line between the feed, the mixture 1 and the solvent\n", "X_F,Y_F=tri(100*m_A/(m_D+m_A),0)\n", "X_M1,Y_M1=tri(XA_M1,XS_M1)\n", "X_S,Y_S=tri(0.,100.)\n", "plt.scatter(X_F,Y_F, color='blue', marker='x')\n", "plt.plot([X_F,X_S],[Y_F,Y_S], color='blue', marker='x')\n", "\n", "#plot the mixture point\n", "plt.scatter(X_M1,Y_M1, color='red', marker='x')\n", "#find the two tie lines bordering the mixture \n", "c1=0\n", "c2=0\n", "for i in range(len(xA_SP)):\n", " if Y_M < YDP[i]+(YSP[i]-YDP[i])*(X_M-XDP[i])/(XSP[i]-XDP[i]):\n", " c1=i-1\n", " c2=i\n", " print ('There will be 2 phases and the mixure is located between the tie lines', c1,'and',c2)\n", " break\n", "if c2==0 : print ('There is only one phase : the separation is impossible')\n", "\n", "#determination of the tie line for the mixture \n", "\n", "#function to find the intersection point between two lines AB and CD\n", "def intersec(xA,yA,xB,yB,xC,yC,xD,yD):\n", " #slope of line A B\n", " AB=(yB-yA)/(xB-xA)\n", " #slope of line A B\n", " CD=(yD-yC)/(xD-xC)\n", " x=-(CD*xC-yC-AB*xA+yA)/(AB-CD)\n", " y=AB*(x-xA)+yA\n", " return x,y\n", "\n", "#find the intersection point I between the two bordering tie line\n", "X_I,Y_I=intersec(XDP[c1],YDP[c1],XSP[c1],YSP[c1],XDP[c2],YDP[c2],XSP[c2],YSP[c2])\n", "#find the intersection point between IM and the binodal curve (diluant side)\n", "X_DC1,Y_DC1=intersec(X_I,Y_I,X_M1,Y_M1,XDP[c2],YDP[c2],XDP[c1],YDP[c1])\n", "#find the intersection point between IM and the binodal curve (solvant side)\n", "X_SC1,Y_SC1=intersec(X_I,Y_I,X_M1,Y_M1,XSP[c2],YSP[c2],XSP[c1],YSP[c1])\n", "plt.plot([X_SC1,X_DC1],[Y_SC1,Y_DC1], color='red', marker='x')\n", "\n", "print ('The composition of the raffinate phase, R1, is :')\n", "xA1,xS1=detri(X_DC1,Y_DC1)\n", "print ('x_A=', round(xA1,2),'% x_S=', round(xS1,2),'% x_D=', round(100-xS1-xA1,2),'%')\n", "print ('The composition of the extract phase, E1, is :')\n", "yA1,yS1=detri(X_SC1,Y_SC1)\n", "print ('y_A=', round(yA1,2),'% y_S=', round(yS1,2),'% y_D=', round(100-yS1-yA1,2),'%')\n", "m_E1=m_M1*(XA_M1-xA1)/(yA1-xA1)\n", "m_R1=m_M1-m_E1\n", "print ('The mass of extract is :', round(m_E1,2), 'g and the mass of raffinate is : ', round(m_R1,2), 'g ')\n", "print ('')\n", "plt.scatter(X_DC1,Y_DC1, color='red', marker='x')\n", "plt.scatter(X_SC1,Y_SC1, color='red', marker='x')\n", "plt.plot([X_SC1,X_DC1],[Y_SC1,Y_DC1], color='red', marker='x')\n", "\n", "#STAGE 2\n", "#calculation of mass fraction\n", "m_M2=m_R1+m_S2\n", "XA_F2=xA1\n", "XA_M2=xA1*m_R1/m_M2\n", "XS_M2=(xS1*m_R1+100* m_S2)/m_M2\n", "\n", "#plot the points and the line between the feed, the mixture 1 and the solvent\n", "X_F2,Y_F2=tri(xA1,xS1)\n", "X_M2,Y_M2=tri(XA_M2,XS_M2)\n", "X_S,Y_S=tri(0.,100.)\n", "plt.scatter(X_M2,Y_M2, color='red', marker='x')\n", "plt.scatter(X_F2,Y_F2, color='blue', marker='x')\n", "plt.plot([X_F2,X_S],[Y_F2,Y_S], color='blue', marker='x')\n", "\n", "#find the two tie lines bordering the mixture \n", "c1=0\n", "c2=0\n", "for i in range(len(xA_SP)):\n", " if Y_M2 < YDP[i]+(YSP[i]-YDP[i])*(X_M2-XDP[i])/(XSP[i]-XDP[i]):\n", " c1=i-1\n", " c2=i\n", " print ('The mixture 2 will lead to 2 phases and the mixure is located between the tie lines', c1,'and',c2)\n", " break\n", "if c2==0 : print ('There is only one phase : the separation is impossible')\n", "\n", "#find the intersection point I between the two bordering tie line\n", "X_I,Y_I=intersec(XDP[c1],YDP[c1],XSP[c1],YSP[c1],XDP[c2],YDP[c2],XSP[c2],YSP[c2])\n", "#find the intersection point between IM and the binodal curve (diluant side)\n", "X_DC2,Y_DC2=intersec(X_I,Y_I,X_M2,Y_M2,XDP[c2],YDP[c2],XDP[c1],YDP[c1])\n", "#find the intersection point between IM and the binodal curve (solvant side)\n", "X_SC2,Y_SC2=intersec(X_I,Y_I,X_M2,Y_M2,XSP[c2],YSP[c2],XSP[c1],YSP[c1])\n", "\n", "\n", "print ('The composition of the raffinate phase, R2, is :')\n", "xA2,xS2=detri(X_DC2,Y_DC2)\n", "print ('x_A=', round(xA2,2),'% x_S=', round(xS2,2),'% x_D=', round(100-xS2-xA2,2),'%')\n", "print ('The composition of the extract phase, E2, is :')\n", "yA2,yS2=detri(X_SC2,Y_SC2)\n", "print ('y_A=', round(yA2,2),'% y_S=', round(yS2,2),'% y_D=', round(100-yS2-yA2,2),'%')\n", "m_E2=m_M2*(XA_M2-xA2)/(yA2-xA2)\n", "m_R2=m_M2-m_E2\n", "print ('The mass of extract is :', round(m_E2,2), 'g and the mass of raffinate is : ', round(m_R2,2), 'g ')\n", "print ('')\n", "plt.scatter(X_DC2,Y_DC2, color='red', marker='x')\n", "plt.scatter(X_SC2,Y_SC2, color='red', marker='x')\n", "plt.plot([X_SC2,X_DC2],[Y_SC2,Y_DC2], color='red', marker='x')\n", "\n", "#STAGE 3\n", "#calculation of mass fraction\n", "m_M3=m_R2+m_S3\n", "XA_F3=xA2\n", "XA_M3=xA2*m_R2/m_M3\n", "XS_M3=(xS2*m_R2+100* m_S3)/m_M3\n", "\n", "#plot the points and the line between the feed, the mixture 1 and the solvent\n", "X_F3,Y_F3=tri(xA2,xS2)\n", "X_M3,Y_M3=tri(XA_M3,XS_M3)\n", "X_S,Y_S=tri(0.,100.)\n", "plt.scatter(X_M3,Y_M3, color='red', marker='x')\n", "plt.scatter(X_F3,Y_F3, color='blue', marker='x')\n", "plt.plot([X_F3,X_S],[Y_F3,Y_S], color='blue', marker='x')\n", "\n", "#find the two tie lines bordering the mixture \n", "c1=0\n", "c2=0\n", "for i in range(len(xA_SP)):\n", " if Y_M2 < YDP[i]+(YSP[i]-YDP[i])*(X_M2-XDP[i])/(XSP[i]-XDP[i]):\n", " c1=i-1\n", " c2=i\n", " print ('The mixture 2 will lead to 2 phases and the mixure is located between the tie lines', c1,'and',c2)\n", " break\n", "if c2==0 : print ('There is only one phase : the separation is impossible')\n", "\n", "#find the intersection point I between the two bordering tie line\n", "X_I,Y_I=intersec(XDP[c1],YDP[c1],XSP[c1],YSP[c1],XDP[c2],YDP[c2],XSP[c2],YSP[c2])\n", "#find the intersection point between IM and the binodal curve (diluant side)\n", "X_DC3,Y_DC3=intersec(X_I,Y_I,X_M3,Y_M3,XDP[c2],YDP[c2],XDP[c1],YDP[c1])\n", "#find the intersection point between IM and the binodal curve (solvant side)\n", "X_SC3,Y_SC3=intersec(X_I,Y_I,X_M3,Y_M3,XSP[c2],YSP[c2],XSP[c1],YSP[c1])\n", "\n", "\n", "print ('The composition of the raffinate phase, R3, is :')\n", "xA3,xS3=detri(X_DC3,Y_DC3)\n", "print ('x_A=', round(xA3,2),'% x_S=', round(xS3,2),'% x_D=', round(100-xS3-xA3,2),'%')\n", "print ('The composition of the extract phase, E3, is :')\n", "yA3,yS3=detri(X_SC3,Y_SC3)\n", "print ('y_A=', round(yA3,2),'% y_S=', round(yS3,2),'% y_D=', round(100-yS3-yA3,2),'%')\n", "m_E3=m_M3*(XA_M3-xA3)/(yA3-xA3)\n", "m_R3=m_M3-m_E3\n", "print ('The mass of extract is :', round(m_E3,2), 'g and the mass of raffinate is : ', round(m_R3,2), 'g ')\n", "print (\"\")\n", "print('The efficiency is ', round((m_E1*yA1+m_E2*yA2+m_E3*yA3)/m_A,2))\n", "print('The efficiency is ', round(100*(m_A-m_R3*xA3/100)/m_A,2), '%')\n", "\n", "plt.scatter(X_DC3,Y_DC3, color='red', marker='x')\n", "plt.scatter(X_SC3,Y_SC3, color='red', marker='x')\n", "plt.plot([X_SC3,X_DC3],[Y_SC3,Y_DC3], color='red', marker='x')\n", "\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.9.12" } }, "nbformat": 4, "nbformat_minor": 2 }