{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Alpha functions\n", "\n", "The attractive parameter of every CEOS has a dependance with temperature, given by an $\\alpha(T)$ function. Normally every CEOS has a default $\\alpha$ function, but the `yaeos` API allows you to modify them. This can be done with the `.set_alpha` method. This method replaces the default alpha function with one defined by the user. \n", "This definition is done with different objects already defined inside `yaeos`.\n", "\n", "The available alpha functions are:\n", "\n", "- AlphaSoave\n", "- AlphaRKPR\n", "- AlphaMathiasCopeman" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## AlphaSoave\n", "\n", "The $\\alpha$ function defined by Soave for the SoaveRedlichKwong EoS:\n", "\n", "$$\n", "\\alpha(T_r)=(1+k(1−\\sqrt{Tr}))^2\n", "$$" ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [ { "data": { "image/png": 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+6I6MA3N3dyckJIRKlSoxZMgQOnbsyLx58y7ZHh4ezt13303Hjh1ZsmRJnmOUL1+ekJCQ3Nf8+fOpVq0a7dq1A+D1118nPDyc2bNn07JlS6pUqcLtt99OtWrVrljX/Pnz8ff3zw1ImzdvxmKx8Oyzz+bu88gjj9CvXz8g7x2YgQMHsnLlSqZNm5Z7d+jQoUMAWK1WxowZQ0BAACEhIbz00ktX/f1p3749w4cPZ8SIEZQtW5bg4GBmzpxJamoqgwYNwsfHh+rVq7Nw4cI8n8vIyODJJ58kKCgIDw8P2rZty/r163O3p6am0r9/f7y9vQkNDeXNN9+87Lkv/k7Dhw8nJiYGi8VC5cqVL9nn/PebNGkSVapUwdPTk0aNGvH999/n67xX8vfff9O+fXs8PT2pXbs2GzZs4MMPP6R79+7XfQwRKUEMA+YNh/RECG2McdN/mPJbNAD3Na9IpUAvGxd4/RRkLmYYkJlqm5dh3HD5np6eZGZmXnbb9u3b+euvv3Bzc7vi5zMzM/n88895+OGHc+fTmDdvHs2bN6d3794EBQXRpEkTZs6cedU6br75ZpKTk9m0aRMAK1eupFy5cqxYsSJ3n5UrV9K+fftLPjtt2jQiIyN59NFHOXHiBCdOnCA8PByAOXPm4OXlxbp165g8eTITJ068JJj925w5cyhXrhx///03w4cPZ8iQIfTu3ZubbrqJjRs3cvvtt/PQQw9x7ty53M+MGTOGH374gTlz5rBx40aqV69O586diY+PB2D06NGsXLmSn3/+md9++40VK1awcePGK9Ywbdo0Jk6cSMWKFTlx4kSeUHSxSZMm8emnnzJjxgx27NjByJEj6devHytXrizQec9bu3Yt7dq1484772Tr1q3UqVOHiRMn8vrrrzNhwoRrfl5ESqBNn8G+JeDsDvfM4K9DSaw9EI+bsxPDb3WcuzGgR0t5ZZ2DV8Nsc+7njoNbwRKwYRgsW7aMxYsXM3z48Nz18+fPx9vbm+zsbDIyMnBycuJ///vfFY8zd+5cEhISGDhwYO66AwcOMH36dEaNGsVzzz3H+vXrefLJJ3Fzc2PAgAGXPY6fnx+NGzdmxYoVNG/enBUrVjBy5EgmTJhASkoKiYmJ7Nu3L/euz78/6+bmRpkyZQgJCcmzrWHDhrz44osA1KhRg//9738sW7aMTp06XfE7NWrUiBdeeAGAsWPH8tprr1GuXDkeffRRAMaPH8/06dPZunUrrVu3JjU1lenTp/PJJ5/QtWtXAGbOnMmSJUuYNWsWQ4YMYdasWXz++efcdtttgBmWKlaseMUa/Pz88PHxwdnZ+ZLvdF5GRgavvvoqS5cuJTIyEoCqVavyxx9/8MEHH9CsWbN8n/e8UaNG0bt3b0aPHg1A37596du3Lz169KBJkybX/LyIlDAJMbDoOfP9rc9jlK/NG9/9BcADrSII8/e0YXH5pyDjwM4HlaysLKxWKw888ECexy0dOnRg+vTppKamMnXqVFxcXOjVq9cVjzdr1iy6du1KWNiFMGe1WmnevDmvvvoqAE2aNGH79u3MmDHjikEGoF27dqxYsYKnnnqK1atXM2nSJL799lv++OMP4uPjCQsLo0aN/KX+hg0b5lkODQ3l5MmT1/0ZZ2dnAgMDadCgQe664OBggNzj7N+/n6ysLNq0aZO7j6urKy1btmTXrl3s37+fzMxMWrVqlbs9ICCAWrVq5eu7/Nu+ffs4d+7cJaEsMzOTJk2aFPi8R48eZc2aNUyZMiV3nYuLC4Zh6G6MSGlktcLPQyEzGcJbQeQwluyMY/ORBDxdnXmiw5WbDdgrBZmLuZYx74zY6tz5dD6ouLm5ERYWhotL3svp5eVF9erVAfj4449p1KgRs2bNYvDgwZcc6/DhwyxdupQff/wxz/rQ0FDq1q2bZ12dOnX44Ycfrlpb+/bt+fjjj9myZQuurq7Url2b9u3bs2LFCs6ePXvZuzHX4urqmmfZYrFgtVrz/ZmL151/hHat4xS1lJQUABYsWECFChXybHN3d899rJVfu3btAqBp06a566Kjo2nZsmWeQCcipcSGWXBwFbh4wt3TycEpt23MoDaVCfLxsHGB+ac2MhezWMzHO7Z4/fMDNT/OB5WIiIhLQsy/OTk58dxzz/HCCy+QlpZ2yfbZs2cTFBTEnXfemWd9mzZtiI6OzrNuz549VKpU6arnO99OZurUqbmh5XyQWbFixWXbx5zn5uaWpydVcapWrRpubm78+eefueuysrJYv349devWpVq1ari6urJu3brc7WfPnmXPnj03dN66devi7u5OTEwM1atXz/MKDw8v8HkTExNxdnbODWzx8fFMmTKFMmXyH5xFxMGd2Q9LxpvvO02EwGr8vPkYe+JS8PVw4f9ucby7MaAgU6r07t0bZ2dn3nvvvTzrrVYrs2fPZsCAAZcEopEjR7J27VpeffVV9u3bx5dffsmHH36YZ5yZyylbtiwNGzbkiy++yA0tt9xyCxs3bmTPnj1XvSNTuXJl1q1bx6FDhzh9+nSx3i3x8vJiyJAhjB49mkWLFrFz504effRRzp07x+DBg/H29mbw4MGMHj2a5cuXs337dgYOHIiT0439VfLx8eHpp59m5MiRzJkzh/3797Nx40beffdd5syZU+DzNm7cmJycHCZPnszu3bvp27cvlStXZufOnRw+fPiGahYRB2LNgblPmG1Bq9wCLR4hM9vK1KXmf4Yeb18NvzKu1ziIfVKQKUVcXFwYNmwYkydPJjU1NXf90qVLiYmJ4eGHH77kMy1atOCnn37iq6++on79+rz88su8/fbbPPjgg9c8X7t27cjJyckNMgEBAdStW5eQkJCrtu14+umncXZ2pm7dupQvX56YmJj8f9kb8Nprr9GrVy8eeughmjZtyr59+1i8eHHu2DlvvPEGN998M926daNjx460bduWZs2a3fB5X375ZcaNG8ekSZOoU6cOXbp0YcGCBVSpUqXA5z0/UOK0adNo0qQJYWFh/Pbbb1SoUIEuXbrccM0i4iD+egeOrAU3H+jxHjg58c36GI7Ep1Hex51BN1WxdYUFZjGMQuj3a8eSkpLw8/MjMTERX19fW5cjIiJSvGK3wYcdwJplhpgm/TiXmU27N1ZwKjmDl3vU46HIyrau8hLX+/Nbd2RERERKquwM+PH/zBBT605obN5N/+SvQ5xKziA8wJM+LSJsXOSNUZAREREpqZa/Aid3gFd56DYNLBYSzmUyfcV+AEZ1qombi2NHAceuXkRERC7v0J/w17vm+27vgHd5AN5fsZ/k9Gxqh/jQo1GFqxzAMSjIiIiIlDTpSfDT44ABTfpB7TsAOJ6Qxid/HQLgma61cXLK/9Af9kZBRkREpKRZNBYSY8A/AjpPyl09dckeMrOttKoSQPua5W1YYOFRkBERESlJdi+AzZ8DFrjnA/Awe/zsiUvmh41HAXi2a+3cgTIdnd0Emddeew2LxcKIESNy16WnpzN06FACAwPx9vamV69exMXF2a5IERERe5ZyCuY9ab6/aThUuil30+RF0VgN6FIvhCYRZW1UYOGziyCzfv16Pvjgg0smBRw5ciS//PIL3333HStXruT48eP07NnTRlWKiIjYMcOAX56Ec6chqB7c+kLupg2H4lm6Kw5nJwuju9zYJLf2xuZBJiUlhQcffJCZM2fmjpwK5hwxs2bN4q233uLWW2+lWbNmzJ49m7/++ou1a9fasGIRERE7tOlziP4VnFyh5wfg4g6AYRi8tnA3APc1r0i18t62rLLQ2TzIDB06lDvvvJOOHTvmWR8VFUVWVlae9bVr1yYiIoI1a9Zc8XgZGRkkJSXleYmIiJRoZw/BomfN97c+DyEXZrdfuuskGw6fxcPVif/cVtM29RWhq0+ZXMS+/vprNm7cyPr16y/ZFhsbi5ubG/7+/nnWBwcHExsbe8VjTpo0iQkTJhR2qSIiIvYpJxt+fAwyUyAiEm56MndTdo6V1xeZd2MGtalCiJ+HraosMja7I3PkyBH+85//8MUXX+DhUXi/sWPHjiUxMTH3deTIkUI7toiIiN1Z/SYcWWdOCHnPDHByzt30XdRR9p1MoWwZV4a0r2bDIouOzYJMVFQUJ0+epGnTpri4uODi4sLKlSt55513cHFxITg4mMzMTBISEvJ8Li4ujpCQkCse193dHV9f3zwvERGREunI37DydfP9nW9C2cq5m1IzsnlryR4Aht9aA18PVxsUWPRs9mjptttuY9u2bXnWDRo0iNq1a/PMM88QHh6Oq6sry5Yto1evXgBER0cTExNDZGSkLUoWERGxH+lJ8MMjYORAg97QqE+ezR+tPsip5AwiAsrQr3UlGxVZ9GwWZHx8fKhfv36edV5eXgQGBuauHzx4MKNGjSIgIABfX1+GDx9OZGQkrVu3tkXJIiIi9mPhM5BwGPwi4I4peTadSs7gg1XmxJBjutRy+Ikhr8amjX2vZerUqTg5OdGrVy8yMjLo3Lkz77//vq3LEhERsa3tP8CWL8HiBD0/BE//PJvfXrqHc5k5NKrox50NQm1TYzGxGIZh2LqIopSUlISfnx+JiYlqLyMiIo4v4QhMbwMZiXDLGLO79UX2nUyh89uryLEafPNYa1pVDbRRoTfmen9+l9x7TSIiIiWNNQd++j8zxFRoDu3GXLLL64t2k2M16Fgn2GFDTH4oyIiIiDiKP9+Gw3+Cmzf0mgnOeXsirdl/hiU7zakInu1asqYiuBIFGREREUdwLAp+f9V833UyBFTNs9lqNfjvrzsBeKBlBNWDfIq7QptQkBEREbF3GSnww6NgzYZ690DjBy7Z5adNx9h+LAkfdxdGdKxhgyJtQ0FGRETE3i0eC/H7wbcC3DUVLJY8m9Myc3hjcTQAT3SoTqC3uy2qtAkFGREREXu2cx5s/BSwwD0fgGfZS3b5aPUBYpPSqeDvyaA2lYu9RFtSkBEREbFXCUdg3nDzfdsRUOXmS3Y5mZTO9JXm4HfPdK2Nh6vzJfuUZAoyIiIi9ign25yCID0BKjSD9s9ddre3lpiD3zUO96dbw5I9+N3lKMiIiIjYo5WvwZG14O4LvWaBi9slu+yOTeLbDUcAGHdXHSz/ajtTGijIiIiI2JsDK2HVP/MndXsbAqpcsothGPx3wS6sBtzZIJRmlQKKt0Y7oSAjIiJiT1JOwY+PAgY0HQD1e112t+W7T7J672ncnJ14pkvt4q3RjijIiIiI2AurFeYOgZQ4KF8burx22d0ys628smAXAA+3rUJEYJnirNKuKMiIiIjYizX/g31LwMUD7p0NbpcPKJ+uOcTB06mU83ZjaIdqxVykfVGQERERsQdHo2DZBPN9l9cguO5ld4tPzWTasr0APH17LXw8XC+7X2mhICMiImJr6Ynw/SBzCoK6d0OzgVfc9a0l0SSnZ1M31JfezcOLrUR7pSAjIiJiS4YBv/wHEg6DfwR0m3bJFATnRccm8+W6GADGd6uLs1Pp6279bwoyIiIitrTxU9jxEzi5QK+PwdP/srsZhsHL83diNaBr/RBaVw0s3jrtlIKMiIiIrZzcBQufMd/fOg7CW1xx1yU74/hjn9ndemzXOsVUoP1TkBEREbGFrDT4bhBkp0G1W+GmJ6+4a3pWDi8v2AnAIzeX7u7W/6YgIyIiYguLxsKpXeAVZM5q7XTlH8mz/jjIkfg0gn3dGdqhejEWaf8UZERERIrbtu8hajZggZ4fgnfQFXc9kZjG/5bvA+C5O+rg5e5STEU6BgUZERGR4nR6r9lLCeDmUVCtw1V3n/TrbtKycmheqSzdG4UVQ4GORUFGRESkuGSlwbcDIDMFKrWF9s9ddff1h+KZt+U4Fgu81L1eqZzd+loUZERERIrLr6Ph5A7wKg/3zgLnKz8myrEavPjzDgDubxFB/Qp+xVWlQ1GQERERKQ6bv4JNnwEW6PUR+IRcdfev18ew80QSvh4uPH17zeKp0QEpyIiIiBS1k7tgwSjzffuxULX9VXdPPJfFlMXRAIzsVJNAb/ciLtBxKciIiIgUpYwUs11M1jmo2gFuefqaH3lzSTRnz2VRM9ibfq0rFUORjktBRkREpKgYBix4Ck5Hg08o9JwJTs5X/ciO44l8vvYwAC91q4ers35UX41+d0RERIrKxk9h69dgcYZ7Pwbv8lfd3Wo1GP/zDqwG3NUwlJuqlyumQh2XgoyIiEhRiN1m9lICuG0cVLrpmh/5cdMxog6fpYybM8/fqfmUroeCjIiISGFLT4Rv+0NOBtToDDf955ofSUzL4rWFuwB48rYahPp5FnWVJYKCjIiISGGyWuGnIRB/APwi4J4ZV51H6bypS/ZwOiWTauW9eLhNlWIotGRQkBERESlMf74N0QvA2Q3umwNlAq75kV0nkvh0zSEAJnSvj5uLfjxfL/1OiYiIFJYDK2D5y+b7O96ACk2v+RHDMBj/83asBtzRIIS2NdTANz8UZERERApD4jH4fjAYVmjcD5oOuK6PfR91lPWHzuLp6swLd9Yt4iJLHgUZERGRG5WdCd8NgHOnIaQB3DkFrmOCx7Opmbz6q9nAd0THGoT5q4FvfinIiIiI3Kjfnoej68HDD+77DFyvL5C8vmg3Z89lUSvYh4fbqoFvQSjIiIiI3Iit38LfH5rv7/kQAq4vkGw4FM/X648A8N976msE3wLS75qIiEhBxe2EX/4ZI+aW0VCry3V9LCvHygtztwPQp3k4zStfu2eTXJ6CjIiISEGkJ8I3/czJIKvdas5qfZ0++fMQu2OTKVvGlWe71i7CIks+BRkREZH8MgyY+wTE7we/cOj50TUngzzveEIaU5fuAWBs1zqU9XIrykpLPAUZERGR/Fr9Juyef2HQO6/A6/7ohF92cC4zhxaVy3Jvs4pFWGTpoCAjIiKSH3t+g+WvmO+7ToYKza77o8t2xbF4RxwuThZeubsBTk7X7qItV6cgIyIicr3O7IcfHgEMaDYQmg+67o+mZebw4rwdAAxuW4VaIT5FU2MpoyAjIiJyPTKS4esHICMRKrY078bkw7vL93L0bBoV/D35T8caRVRk6aMgIyIici2GAXOHwKnd4B0CfT4DF/fr/vjeuGQ+XHUAgBe71aWMm0tRVVrqKMiIiIhcy+opsOsXcHI1Q4xPyHV/1Go1ePbHbWRbDTrWCeL2etf/Wbk2BRkREZGr2bMYlv/XfH/nFAhvma+Pf/F3DFGHz+Ll5syEHvWLoMDSTUFGRETkSs7shx8exWzcO8hs4JsPJxLTeH3hbgBGd65FBU0KWegUZERERC7n4sa94a3y3bjXMAzGzd1BSkY2TSL8eSiyctHUWcopyIiIiPyb1Qo/PW427vUJhfs+BZf8jcC7cHssS3fF4eps4bWeDXHWmDFFQkFGRETk3/KM3Ju/xr0AieeycseMGdKumsaMKUIKMiIiIheLXgS//9O4944pEN4i34eYtHAXp5IzqFreiyc6VC/kAuViCjIiIiLnndx1YeTe5g9DswH5PsTaA2f4ev0RAF7r2RAP1+ubTFIKRkFGREQEIPUMfHU/ZCZDpbbQ5fV8HyI9K4exP24D4IFWEbSsElDYVcq/KMiIiIhkZ8K3/eHsIfCvVKDGvWBOQ3DwdCpBPu4827V24dcpl1CQERGR0s0wYOEYOPwHuHnDA9+AV2C+D7PrRBIfrDSnIZjYoz6+Hq6FXalchoKMiIiUbus/gqjZgAV6zYKgOvk+RI7V4NkftpJtNehSL4Qu9TUNQXFRkBERkdJr/++w8BnzfacJUKtLgQ4z569DbDmaiI+HCxN61CvEAuVaFGRERKR0OrMfvhsARg406gs3PVmgwxw+k8obi6MBeLZrbYJ9PQqzSrkGBRkRESl90hLgyz6QnggVW8Jdb4Ml/yPvWq0Go7/fSlpWDpFVA+nbIqLQS5WrU5AREZHSJScbvn8YzuwF34rQ53NwLdhdlE/XHOLvg/GUcXNm8r0NcdI0BMVOQUZEREqXJeNg/zJwLQN9vwSf4AId5vCZVF5fZD5SGtu1NuEBZQqzSrlONg0y06dPp2HDhvj6+uLr60tkZCQLFy7M3Z6ens7QoUMJDAzE29ubXr16ERcXZ8OKRUTEoUXNgbXvm+/vmQGhjQp0mH8/UnqwVaVCLFLyw6ZBpmLFirz22mtERUWxYcMGbr31Vnr06MGOHeZEWyNHjuSXX37hu+++Y+XKlRw/fpyePXvasmQREXFUh/6EBU+Z7zs8D3V7FPhQn609rEdKdsJiGIZh6yIuFhAQwBtvvMG9995L+fLl+fLLL7n33nsB2L17N3Xq1GHNmjW0bt36uo6XlJSEn58fiYmJ+Pr6FmXpIiJir+IPwEcd4dwZqNcT7v24QI17wXyk1OXt1aRl5fByj3o8FFm5cGsV4Pp/fttNG5mcnBy+/vprUlNTiYyMJCoqiqysLDp27Ji7T+3atYmIiGDNmjVXPE5GRgZJSUl5XiIiUoqlnYUv7jNDTFgT6PFegUOM1Wow5p9HSq2rBuiRkh2weZDZtm0b3t7euLu78/jjj/PTTz9Rt25dYmNjcXNzw9/fP8/+wcHBxMbGXvF4kyZNws/PL/cVHh5exN9ARETsVnYmfPPQhR5Kfb8Gt4I3yv1s7WHWnX+k1KuRHinZAZsHmVq1arF582bWrVvHkCFDGDBgADt37izw8caOHUtiYmLu68iRI4VYrYiIOAzDgPkj4NBqcPOBB78Fn4JPHRBz5hyvLdwNmAPfRQSql5I9cLF1AW5ublSvXh2AZs2asX79eqZNm0afPn3IzMwkISEhz12ZuLg4QkKu/AfR3d0dd3f3oi5bRETs3eo3YfMXYHGC3rMhuOBTB5i9lLbkPlLqp0dKdsPmd2T+zWq1kpGRQbNmzXB1dWXZsmW526Kjo4mJiSEyMtKGFYqIiN3b/iMsf9l833Uy1Oh0Q4f7fJ35SMnTVY+U7I1N78iMHTuWrl27EhERQXJyMl9++SUrVqxg8eLF+Pn5MXjwYEaNGkVAQAC+vr4MHz6cyMjI6+6xJCIipdCR9fDT4+b71k9Ay0dv6HAxZ84x6Vc9UrJXNg0yJ0+epH///pw4cQI/Pz8aNmzI4sWL6dTJTM5Tp07FycmJXr16kZGRQefOnXn//fdtWbKIiNizs4fgq/shJwNq3QG3v3JDh7NaDcb8YD5SalUlgIda65GSvbG7cWQKm8aREREpJdISYNbtcDoaQhrCoIXg7n1Dh/xo9QFeWbALT1dnFo24mUqBXoVTq1yTw40jIyIiUmDZmfBNPzPE+ITBA9/ccIjZG5fM5MXmXErP31lHIcZOKciIiIhjMwyYN+yfbtbeZojxDbuhQ2ZmWxn57WYys620r1WeB1tFFFKxUtgUZERExLEtfxm2fgMWZ7hvDoQ2vOFD/m/5XrYfS8K/jCuTezXEUsCRgKXoKciIiIjj2vCxOV4MQPd3oHrHq+9/HTbFnOW9FfsBeOXu+gT5etzwMaXoKMiIiIhjil50YTbr9mOhSb8bPmRaZg6jvt1CjtWgR+Mw7mp4Y4+opOgpyIiIiOM5FgXfDwLDagaYds8UymEnLdzFwdOphPh6MLF7/UI5phQtBRkREXEs8Qfhyz6QdQ6q3QZ3vV3g2awv9nv0ST5dcxiAN3o3xK+M6w0fU4qegoyIiDiOc/Hwxb2QegpCGpiNe51vPHCcTslg9HdbABh4U2VurlH+ho8pxUNBRkREHENWmjlq75l94BcOD3wH7j43fFjDMBj93RZOp2RSK9iHZ7vWLoRipbgoyIiIiP2z5sCPj8GRdeDuBw9+B76hhXLoz9Ye5vfoU7i5ODGtb2M8XJ0L5bhSPBRkRETEvhkGLBwDu+aBkyvc/wUE1SmUQ++JS+a/C3YBMLZrbWqHaCobR6MgIyIi9m3lZFj/EWCBnh9ClZsL5bDpWTk8+dUmMrKttKtZnoE3VS6U40rxUpARERH7teFjWPGq+b7rZKjfs9AOPXlRNLtjkwn0cmNK70YavddBKciIiIh92jnvwoB3t4yGVo8V2qFX7jnFx38eBMyu1uV93Avt2FK8FGRERMT+HFwNPww2B7xrOgA6PF9ohz6TksHT/3S17h9ZiVtrBxfasaX4KciIiIh9ObEVvn4AcjKh9l1w51uFMuAdmF2tx3y/lVPJGdQM9ua5Owqn0bDYjoKMiIjYj/iD5oB3GUlQqQ30mgXOLoV2+M/XxbBs90ncnJ2Ydn8TdbUuARRkRETEPqScgs97QkocBNeH+78E18KbeXpvXDKvzN8JwDNda1MnVF2tSwIFGRERsb2MZPiiF8QfAP8IePB78PQvtMOnZeYw7Euzq/UtNcszSF2tSwwFGRERsa3sDPj6QTixBcoEQr+fCm3U3vMm/LKD6Lhkynm7M6V3Q5yc1NW6pFCQERER28nJNnsnHVwJrl7mnZhy1Qv1FD9vPsbX649gscC0+xsT5FN4j6vE9hRkRETENqxWmDccdv0Czm7m1AMVmhbqKQ6cSuG5H7cBMPzWGrSpXq5Qjy+2l+8gk5WVhYuLC9u3by+KekREpDQwDFj0LGz5EizOcO9sqNahUE+RnpXD0C83kZqZQ+uqAfznthqFenyxD/kOMq6urkRERJCTk1MU9YiISGnw+3/h7w/M93e/D3XuKvRTvDx/J7tOJBHo5ca0+5vgrHYxJVKBHi09//zzPPfcc8THxxd2PSIiUtL9+Q6sesN8f8cUaHR/oZ9i/tbjfLEuBosFpvZpTLCv2sWUVAUaZeh///sf+/btIywsjEqVKuHl5ZVn+8aNGwulOBERKWE2zIYl48z3t42Hlo8W+ikOnU7l2R/MdjFPtK/GLTXLF/o5xH4UKMjcfffdhVyGiIiUeNu+h/kjzfdtR8LNTxX6KTKycxj21UZSMrJpWTmAkR1rFvo5xL4UKMi8+OKLhV2HiIiUZNGL4Kf/Awxo8QjcVjQ/Ryb9upvtx5IoW8aVaX0b4+Kszrklna6wiIgUrYOr4Nv+YM2Ghn2g6xuFNgnkxRZtP8Enfx0C4K0+jQn18yz0c4j9KdAdmZycHKZOncq3335LTEwMmZmZebarEbCIiABwdAN8eT/kZECtO6HH++BU+P+HPhJ/jtHfbwXg/9pVpUOtoEI/h9inAv1pmjBhAm+99RZ9+vQhMTGRUaNG0bNnT5ycnHjppZcKuUQREXFIcTvg816QlQpV2sG9HxfqTNbnZWTnMOzLjSSnZ9OsUlmevr1WoZ9D7FeBgswXX3zBzJkzeeqpp3BxcaFv37589NFHjB8/nrVr1xZ2jSIi4mhO7YFPe0B6AlRsWegzWV/spXk72XI0Ef8yrrzTtwmuahdTqhToasfGxtKgQQMAvL29SUxMBOCuu+5iwYIFhVediIg4njP7YU43SD0FIQ3hwW/B3btITvXt+iN89bc5Xsw79zehgr/axZQ2BQoyFStW5MSJEwBUq1aN3377DYD169fj7u5eeNWJiIhjOXvIDDEpsRBUDx6aC55li+RUW48m8MLP5nQ5T3WqqfFiSqkCBZl77rmHZcuWATB8+HDGjRtHjRo16N+/Pw8//HChFigiIg4i4Qh80g2SjkG5WtD/Z/AKLJJTxadmMuTzjWRmW+lYJ4gn2hfujNniOCyGYRg3epA1a9awZs0aatSoQbdu3QqjrkKTlJSEn58fiYmJ+Pr62rocEZGSKek4zL4Dzh6EgGow6FfwCSmSU+VYDQbO/pvVe09TObAMPw9ri5+na5GcS2znen9+F0rz8cjISCIjIwvjUCIi4miS42BOdzPE+FeCAb8UWYgBeGtJNKv3nsbT1ZkPHmquEFPKFTjIREdH8+6777Jr1y4A6tSpw/Dhw6lVS93eRERKjdTTZu+kM3vBL9wMMX4Viux0v+2I5b3f9wPwWq8G1ArxKbJziWMoUBuZH374gfr16xMVFUWjRo1o1KgRGzdupH79+vzwww+FXaOIiNijc/Hw6d1wahf4hMGAeVC2UpGd7sCpFJ76dgsAg9pUpkfjogtM4jgK1EamWrVqPPjgg0ycODHP+hdffJHPP/+c/fv3F1qBN0ptZEREisC5ePi0O8RuA68gs01MuRpFdrrUjGzuef9P9sSl0LJyAF882krjxZRw1/vzu0B/Ck6cOEH//v0vWd+vX7/cbtkiIlJCpZ4x28ScDzEDfinSEGMYBs/8sJU9cSkE+bjzvwc16J1cUKA/Ce3bt2f16tWXrP/jjz+4+eabb7goERGxU6lnzDsxcf+EmIHzIah2kZ5y1h8Hmb/1BC5OFt5/sClBPkUzQrA4putu7Dtv3rzc9927d+eZZ54hKiqK1q1bA7B27Vq+++47JkyYUPhVioiI7aWeNu/EnNwB3sEwYD6Ur1mkp1x74AyTFu4G4IU769C8ckCRnk8cz3W3kXG6ztlKLRYLOTk5N1RUYVIbGRGRQmCDEHMiMY1u7/7B6ZRM7m4cxtQ+jbFYLEV6TrEfhT6OjNVqLZTCRETEwaScMh8nndwJ3iHm46QibBMDkJ6Vw2OfRnE6JZPaIT5M6tlQIUYuq/DnUxcRkZIj5ZQ5d9KpXeATat6JKVe00wEYhsHo77ey7VgiZcu4MrN/czzdnIv0nOK4FGREROTy/h1iBi6AwGpFftr3V+znly3HcXGyML1fM8IDyhT5OcVxKciIiMilkk6Yj5NO7zEHuxs4v1hCzJKdcUz5LRqACT3q0bpq0Uw6KSWHgoyIiOSVEHNh7iTfCuY4McUQYqJjkxnx9SYMAx5qXYkHWxXdKMFScuRrHJnly5fbVY8kEREpZGf2X5jF2r8SDFpYLCEmPjWTRz5dT2pmDpFVAxnfrW6Rn1NKhnwFmUceeYTy5cvzwAMP8M0335CUlFRUdYmISHE7FW2GmMQjEFgDHl5UpHMnnZeVY+WJL6I4Ep9GREAZ3n+wqUbuleuWrz8pBw4cYMWKFdStW5c333yT4OBgOnXqxLvvvktMTExR1SgiIkUtdpsZYlJiIaieOXeSb1ixnHrCLztYeyAeb3cXPhrQnLJebsVyXikZCjRp5HnHjx9n3rx5zJs3j99//51atWrRvXt3unfvTvPmzQuzzgLTgHgiItdwLAo+6wnpCRDaCB6aC2WKZwTdz9YeZtzc7Vgs8FH/5txWJ7hYziv2r0gnjTwvLCyMxx9/nF9//ZXTp08zbtw4Dh06RJcuXXj11Vdv5NAiIlIcDq+BOT3MEFOxJfSfV2whZtWeU7w0bwcAYzrXVoiRArmhOzJXkpOTQ3x8POXLly/sQ+eb7siIiFzBgZXw1f2QdQ4q3wx9vwZ372I5dXRsMr2m/0VKRjY9m1TgzfsaaeReyaPQpyjID2dnZ7sIMSIicgV7foNv+kFOBlS7Dfp8Dm7FM/DcyeR0Hv5kPSkZ2bSqEsCkXg0UYqTA1CxcRKS02f4DfP2AGWJq3Ql9vyq2EJOWmcMjczZwLCGNquW8+OChZri7aPoBKTgFGRGR0mT9LPh+MFizoH4vuG8OuLgXy6lzrAYjvtnE1qPmHEofD2yBfxn1UJIboyAjIlIaGAasegMWjAIMaD4Yes4EZ9diK+G1hbtYvCMON2cnZvZvTuVyXsV2bim58hVkrFYrr7/+Om3atKFFixY8++yzpKWlFVVtIiJSGKxWWPw8LH/FXL5lNNz5JjgV3yOdz9ceZubqgwC80bshzSsXT88oKfnyFWT++9//8txzz+Ht7U2FChWYNm0aQ4cOLaraRETkRuVkw89DYe175nLnSXDrC1CMjWtXRJ/kxX+6WT/VqSY9GlcotnNLyZevIPPpp5/y/vvvs3jxYubOncsvv/zCF198gdVqLar6RESkoLLS4dv+sOVLsDjD3TMg8oliLWF3bBLDvtxEjtWgV9OKDLu1erGeX0q+fAWZmJgY7rjjjtzljh07YrFYOH78eKEXJiIiNyA9Cb64F6IXgLO72b26cd9iLSEuKZ2HZ5vdrFtXDWBST3WzlsKXryCTnZ2Nh4dHnnWurq5kZWUV6OSTJk2iRYsW+Pj4EBQUxN133010dHSefdLT0xk6dCiBgYF4e3vTq1cv4uLiCnQ+EZFSIfU0zOkGh1aDmw889CPUvuPanytESelZDPj4b44nplO1vBcz+jXDzUX9S6Tw5WtAPMMwGDhwIO7uF7rqpaen8/jjj+PldaH1+Y8//nhdx1u5ciVDhw6lRYsWZGdn89xzz3H77bezc+fO3OONHDmSBQsW8N133+Hn58ewYcPo2bMnf/75Z35KFxEpHRKOwGf3wJm9UKYc9PsBwhoXawnpWTk89ukGdscmU87bnU8GtlQ3ayky+ZqiYNCgQde13+zZswtUzKlTpwgKCmLlypXccsstJCYmUr58eb788kvuvfdeAHbv3k2dOnVYs2YNrVu3vuQYGRkZZGRk5C4nJSURHh6uKQpEpOQ7uRs+7wVJR8EvHB76CcrVKNYScqwGw7/ayK/bYvF2d+Hrx1pTv4JfsdYgJUORTFFQ0IByvRITEwEICDC75UVFRZGVlUXHjh1z96lduzYRERFXDDKTJk1iwoQJRVqniIjdObwGvuoD6YlQrqYZYvwqFmsJhmEw8Zcd/LotFldnCx8+1EwhRoqc3TywtFqtjBgxgjZt2lC/fn0AYmNjcXNzw9/fP8++wcHBxMbGXvY4Y8eOJTExMfd15MiRoi5dRMS2ds6DT3uYIaZiS3h4cbGHGID3V+xnzprDWCzw1n2Nual6uWKvQUqfIpk0siCGDh3K9u3b+eOPP27oOO7u7nna8IiIlGh/z4RfRwMG1LoDes0qtnmTLvbthiO8sdjsrDH+rrp0axRW7DVI6WQXd2SGDRvG/Pnz+f3336lY8cL/IkJCQsjMzCQhISHP/nFxcYSEhBRzlSIidsQwYOkE+PVpwIBmg+C+z2wSYpbvjmPsj9sAeLxdNQa1qVLsNUjpZdMgYxgGw4YN46effmL58uVUqZL3D3+zZs1wdXVl2bJlueuio6OJiYkhMjKyuMsVEbEPOVkwdwj88Za53OF5uGsqOBf/TfaNMWd54ouN5FgNejatwDNdahV7DVK62fTR0tChQ/nyyy/5+eef8fHxyW334ufnh6enJ35+fgwePJhRo0YREBCAr68vw4cPJzIy8rINfUVESryMZPh2AOxfZo7W220aNH3IJqXsO5nCw5+sJz3LSrua5Xm9V0MNeCfFLl/drwv95Ff4Az979mwGDhwImOPUPPXUU3z11VdkZGTQuXNn3n///et+tHS93bdEROxe0gmzZ9KJLeBaBnrPgZq326SUuKR0er7/F8cS0mhU0Y8vH22Nl7vdNLuUEuB6f37bNMgUBwUZESkR4nbAF/eZY8SUKQcPfAsVm9mklPjUTPp8sIa9J1OoUs6L7x+PJNBbnSykcBXJODIiImID+5aZj5MykyGwBjz4HQTYpkFtUnoW/T9ex96TKQT7uvPpwy0VYsSmFGREROxZ1CcwfxQYOVCpLfT5DMoE2KSUc5nZPDx7PduPJRHo5cYXj7QmPKD4e0mJXExBRkTEHlmtsHwi/DHVXG54P3R/F1xsM2dRelYO//dZFBsOn8XXw4VPB7ekepC3TWoRuZiCjIiIvclKN7tX7/hnAt72Y6HdM2CjHkFZOVaGfbmJ1XtPU8bNmU8ebkm9ME09IPZBQUZExJ6knoGv+8KRdeDkat6FadzXZuXkWA2e+nYLS3fF4ebixEf9m9M0oqzN6hH5NwUZERF7cWqP2b06/gB4+EGfL6DKzTYrxzAMnv9pG/O2HMfFycKMfk01f5LYHQUZERF7sG8ZfDcIMhLBv5LZM6m87UbJNQyDl+fv4uv1R3CywLT7m3Br7WCb1SNyJQoyIiK2ZBiw7gNYPBYMK0REQp/Pwcu2dz6mLtnDx38eBOD1Xg25s2GoTesRuRIFGRERW8nJMid9jPrEXG7cD+56C1xsOy7LByv3887yfQBM6F6P3s3DbVqPyNUoyIiI2MK5ePi2PxxaDVjg9pchcpjNeiad99maQ0xauBuAMV1qMeCmyjatR+RaFGRERIrbqWj4sg+cPQhuPnDvLKjZ2dZV8cW6w4z7eQcAQztU44n21W1ckci1KciIiBSnvUvh+0GQkWQ26n3gGwiqY+uq+GLdYZ7/aTsAj7StwtO3266hsUh+KMiIiBQHw4C10+G35/9p1HuTOd2AjRv1wqUh5vk762Cx8SMukeulICMiUtSy0mHBU7D5c3O5ST+4c6rNphu42JfrYhRixKEpyIiIFKXEo/BNPzi+CSxO0OlliBxq80a9YIaY537aBsBghRhxUAoyIiJF5dCf8N0ASD0FnmXh3tlQrYOtqwIuDTEvKMSIg1KQEREpbIYBf38Ii58DazaENDAHuStb2daVAQoxUrIoyIiIFKasNJg/ErZ8ZS7Xv9ec+NGtjG3r+sdnaw8zbq7ZJkYhRkoCBRkRkcKScMRsD3Nis921hwH4cNV+Xv3VHOxOIUZKCgUZEZHCcHA1fDcQzp0GzwDo/QlUbWfrqgBzAsi3l+5l2rK9gDnY3dO311KIkRJBQUZE5EYYBqybAYufByMHQhrC/V+Af4StKwPMEDNp4W4+XHUAgNGdazG0g0bslZJDQUZEpKAyUmD+CNj2nbncsA90mwaunjYt6zyr1WD8vO18vjYGgPF31eXhtlVsXJVI4VKQEREpiFPR5qSPp3aDxRk6/xdaPW437WGyc6w888M2fth4FIsFJt3TgPtb2sddIpHCpCAjIpJf276HeU9CVir4hJrjw1SKtHVVuTKzrYz8ZjMLtp3A2cnCW/c1okfjCrYuS6RIKMiIiFyv7Az47QVzjBiAKrdAr1ngHWTbui6SnpXD0C82smz3SVydLbzbtyld6ofYuiyRIqMgIyJyPRJizF5Jx6LM5Zufgg7Pg5OzTcu6WHJ6Fo99GsWaA2dwd3Hig4ea0b6W/YQskaKgICMici17l8KPj0DaWfDwh54fQs3Otq4qj5PJ6Qz8eD07TyTh7e7CzP7NiawWaOuyRIqcgoyIyJXkZMHv/4U/pprLoY3hvk+hbCWblvVvh8+k8tCsv4mJP0c5bzc+GdSS+hX8bF2WSLFQkBERuZyEI/D9w3D0b3O5+cPQeRK4eti2rn/ZfiyRgbP/5nRKJhEBZfj04ZZULudl67JEio2CjIjIv+1eAHOfgPQEcPeF7u9AvXtsXdUl/tp3msc+iyIlI5u6ob588nALgnzsK2iJFDUFGRGR87IzYMmLsG66uRzWFO79GALsbxC5BVtPMPKbzWTmWGldNYAP+zfH18PV1mWJFDsFGRERgDP74ftBcGKLuRw5DG57EVzcbFvXZXy25hDj5+3AMKBr/RCm9mmMh6v99J4SKU4KMiIi23+Aef+BzGTwLAt3T4daXW1d1SUMw2Dqkj28s3wfAA+2imBij/o4O9nHaMIitqAgIyKlV0YyLHwWNn9uLkdEQq+PwK+ibeu6jKwcK+N/3s5Xfx8BYETHGvznthqawVpKPQUZESmdjkbBD4Ph7EHAYg5w134sONvfP4tJ6VkM/WIjq/eexmKBl3vUp19r++oCLmIr9vc3VkSkKFlz4I+34PdJYOSAb0Xo+QFUbmvryi7r6NlzPPzJevbEpeDp6sw7fZvQqW6wrcsSsRsKMiJSeiTEwI//BzF/mcv17oG7pprtYuzQ5iMJPDJnA6dTMgjycWfWgBY0qKiB7kQupiAjIqXDtu9h/ijISAQ3b7jjDWjUF+y0jcmi7ScY8c1m0rOs1A7x4eOBLQjz97R1WSJ2R0FGREq29CT4dTRs/dpcrtAces2EgKq2resKDMNg5uoDTFq4G8OADrXK8+4DTfF21z/XIpejvxkiUnIdXgM//R8kHAaLE9z8NLQbA872OXCc2TNpB1/9HQNA/8hKjL+rLi7OTjauTMR+KciISMmTlQ6/vwJ//Q8wwC/CnLG6UqStK7uif/dMGndnXQa1qazu1SLXoCAjIiXL8U3w0+Nware53LgfdHkVPOy3kax6JokUnIKMiJQMOVmw+k1Y9QZYs8ErCLpNg9p32Lqyq9pwKJ7HP4/idEomwb5mz6T6Few3dInYGwUZEXF8J3eZbWHOz5NU92648y3wCrRpWdfy9d8xjPt5O1k5BnVCffl4YHNC/dQzSSQ/FGRExHFZc2DNe7D8FcjJAA9/uPNNaHCvrSu7qqwcK/9dsItP/joEwJ0NQnmjd0PKuOmfZJH80t8aEXFM8Qdg7hMQs8ZcrnE7dHsHfENtW9c1nE3NZOiXG/lr/xkAnupUk2G3VlejXpECUpAREcdizYH1H8HSCZCVag5u12USNHnIbge3O293bBKPfrqBI/FpeLk5M7VPY26vF2LrskQcmoKMiDiOk7th3nA4+re5XPlm6PEelLX/CRTnbjrGsz9uJT3LSkRAGWb2b06tEB9blyXi8BRkRMT+ZWfCn9Ng1WTIyQQ3H+g0AZoNAif7HiwuM9vKfxfsZM6awwDcUrM80/o0pqyXm40rEykZFGRExL4d22jehYnbbi7X6Ax3vQV+FW1b13U4kZjG0C82sjEmAYAnb63OfzrWxNnJvh+BiTgSBRkRsU+Z52DFq2avJMMKZQKh62So38vu28IA/LX/NE9+tYnTKZn4ergwtU9jbqujQe5ECpuCjIjYn4OrYN6TcPagudygN3R5DbzK2bau62AYBh+sOsDkRbuxGlAn1JcZ/ZpSKdDL1qWJlEgKMiJiP9ITYcl4iPrEXPatAHdNhZqdbVrW9UpOz2L0d1tZtCMWgF5NK/LK3fXxdHO2cWUiJZeCjIjYnmHArnmw8BlIPmGuaz4YOr4EHr42Le167YlL5vHPojhwOhVXZwsvda/HAy0jND6MSBFTkBER2zp7CH4dDXt/M5cDqkH3d6FyG5uWdb0Mw+Crv48wcf4O0rOshPp58P6DTWkSUdbWpYmUCgoyImIb2Zmw5n+wcjJkp4GTK7QdCTePAlfHmG8oMS2L537cxoJt5l2kW2qWZ+p9jQj0drdxZSKlh4KMiBS/w3/B/JFware5XPlmc5LH8jVtW1c+bIw5y5NfbeLo2TRcnCyM6VKLR9pWxUldq0WKlYKMiBSf1DNmY97Nn5vLZcpB51eh4X0O0aUawGo1eyVN+S2aHKtBREAZ3unbhMbh/rYuTaRUUpARkaJnzYGNn8KyiZAWb65rNgg6vgiejtOW5GRyOk99u4XVe08DcFfDUF7t2QBfD1cbVyZSeinIiEjROrIefn0aTmw2l4Prm12qw1vatKz8WrXnFKO+3czplEw8XJ2Y0L0e9zUPV68kERtTkBGRopFyEpa+BJu/MJfdfaHDc9DiEXB2nDsYWTlWpvwWzQcrDwBQO8SHd/s2oUawJnwUsQcKMiJSuHKy4O8PYcVrkJFkrmvcz3yM5B1k29ryaf+pFEZ9s5ktRxMBeKh1JZ6/sw4erhrgTsRe2HTa2FWrVtGtWzfCwsKwWCzMnTs3z3bDMBg/fjyhoaF4enrSsWNH9u7da5tiReTaDqyEGW1h8XNmiAlrAo8sg7vfc6gQYxgGn605xJ3vrGbL0UR8PVyY0a8pL99dXyFGxM7YNMikpqbSqFEj3nvvvctunzx5Mu+88w4zZsxg3bp1eHl50blzZ9LT04u5UhG5qrOH4dsB8Gl3s0u1ZwB0ewceWQ4Vm9u6unyJS0pnwOz1jPvZHOCubfVyLB55C13qh9q6NBG5DJs+WuratStdu3a97DbDMHj77bd54YUX6NGjBwCffvopwcHBzJ07l/vvv784SxWRy0lPgj/egjXvQ04GWJzMqQU6PAdlAmxdXb79uu0Ez/20jYRzWbi7ODG2a236R1bW2DAidsxu28gcPHiQ2NhYOnbsmLvOz8+PVq1asWbNmisGmYyMDDIyMnKXk5KSirxWkVInJxs2fQa//xdST5nrKt8MXSZBSAPb1lYA8amZvDhvB79sOQ5A/Qq+TL2vsRr0ijgAuw0ysbHm7LHBwcF51gcHB+duu5xJkyYxYcKEIq1NpFTbvxwWPw8nd5rLgdXh9legZheHGdTuYr9uO8G4uds5k5qJkwWGtK/Gf26riZuLTZ+8i8h1stsgU1Bjx45l1KhRuctJSUmEh4fbsCKREuJUNPz2woXJHT38of1YaP4wuLjZtLSCOJ2SwYs/78idJ6lWsA9v9G5Iw4r+ti1MRPLFboNMSEgIAHFxcYSGXmhkFxcXR+PGja/4OXd3d9zdNWGbSKFJPQMrJsGGj8HIAScXaPl/cMvTDtkOxjAM5m89wYvzdhCfmomzk4Un2ldj2K3VcXdRjyQRR2O3QaZKlSqEhISwbNmy3OCSlJTEunXrGDJkiG2LEykNMlNh7fvw5zsXxoOpfRd0mgiB1WxbWwGdTE5n3NztLN4RB5iD203p3Yj6FfxsXJmIFJRNg0xKSgr79u3LXT548CCbN28mICCAiIgIRowYwSuvvEKNGjWoUqUK48aNIywsjLvvvtt2RYuUdDlZEPUJrJwMqSfNdSENofN/ocotNi2toAzD4OfNx3nplx0knMvCxcnC0A7VGdqhutrCiDg4mwaZDRs20KFDh9zl821bBgwYwCeffMKYMWNITU3lscceIyEhgbZt27Jo0SI8PDxsVbJIyWW1wo4fYfkrcPagua5sZbh1HNTrCU6O+QP/6NlzjP95B8t3m6Gsbqgvb/RuSL0w3YURKQkshmEYti6iKCUlJeHn50diYiK+vr62LkfE/hgG7F8GSydA7FZznVcQtBsDTQc4ZENegOwcK5/8dYi3luzhXGYOrs4Wnry1Bo+3r4ars2OGMpHS5Hp/ftttGxkRKQZHN5gTOx5abS67+UCb/0DrIeDubdPSbsT2Y4k8++NWth8z2/a0rBzAqz3rUz1I48KIlDQKMiKl0aloWDYRds83l53doOVj0HYUeAXatrYbkJyexdtL9zL7z4NYDfD1cGHsHXXo0zxco/OKlFAKMiKlyem9sPJ12PY9YJhTCjTqa44H4++44y2db8z73193cSrZHNn7roahjO9WlyAftakTKckUZERKgzP7YdUbsPUbMKzmutp3wa0vQFAd29Z2g6Jjkxn383b+PhgPQJVyXrzUvR7tapa3cWUiUhwUZERKsrOHzACz+StzMDuAml2h/bMQ1tiWld2w5PQspi3dy+y/DpFjNfBwdWL4rTV45OYqGthOpBRRkBEpic4eNmel3vQ5WLPNdTVuNwNMhWa2re0GGYbBvC3H+e+CXZz85zFS53rBjLurLhXLlrFxdSJS3BRkREqS0/vMALP1mwsBptqt0P45CG9h29oKwY7jiUz8ZSfr/nmMVDmwDC91r0f7WkE2rkxEbEVBRqQkiNsBq9+EHT9daANTtT20exYqRdq0tMJwMimdKb9F813UUQwDPFydGNahOo/eUlWPkURKOQUZEUd2fBOsmnKhGzWYbWBueRoqNrddXYUkLTOHmasPMGPlfs5lmm18ujUK45kutfQYSUQABRkRxxSz1gww+5b8s8ICdbvDzU9DaEObllYYrFaDn7ccY/KiaE4kpgPQJMKfF+6sS7NKZW1cnYjYEwUZEUdhtcKeheZs1EfWmussTtCgtzmQXVBt29ZXSNYfiueV+TvZcjQRgAr+njzTtTbdGoZisWhQOxHJS0FGxN5lZ5iNd/98B87sNdc5u0HDPtB2JARWs219heTQ6VTeWBzNgm0nAPByc+aJDtUZ3LYKHq5qByMil6cgI2Kv0hJgw8ewbgakxJnr3P2g+SBo9Tj4htq0vMJyMjmdd5ft46u/Y8i2GjhZoE+LcEZ1qkV5H3dblycidk5BRsTeJB6Dte9D1CeQmWKu8wmDyCfM2ag9SsYs7snpWXy46gAfrT5IWpbZkLddzfI827U2dUJLxncUkaKnICNiL45FwdoZsOPHC2PAlK9jzkZdvxe4uNm2vkKSlpnDZ2sPMX3Ffs6eywKgUbg/z3apTWQ1x52wUkRsQ0FGxJZysmDXPDPAHP37wvrKN8NNT0KNTlBCGrimZ+XwxboYpq/Yz+kUc0TequW9GNO5Fp3rhaghr4gUiIKMiC2ci4eo2fD3R5B83Fzn5GreeWn9OIQ1sW19hSgjO4dv1h/hvd/3EZdkBpjwAE+G31qDnk0q4OLsZOMKRcSRKciIFKe4nbBuOmz9FrLN8VHwKg/NB0Pzh8En2Lb1FaLMbCvfRR3hveX7OP7PWDAV/D0Zdmt17m1WEVcFGBEpBAoyIkUtJxv2LjZ7Hx1cdWF9aCNoNQTq9wSXktM7JzPbyk+bjvLu8n0cPZsGQIivB0Nvrc59zStqSgERKVQKMiJFJTkWNn5q9j5KOmauszhBnW5mgIloXWLav4DZBubbDUeYsWJ/7h2Y8j7uDG1fjftbRmgsGBEpEgoyIoXJMODQalj/EexecKH3UZlAaNIPWjwK/uG2rbGQpWZk8+W6GD5cfYBTyWYbmPI+7vzfLVXp17qSAoyIFCkFGZHCcC7eHH13w8dwes+F9eGtoMUjUKc7uHrYrr4icDolgzl/HeLTNYdJTDO7UVfw9+TxdlXp3TxcAUZEioWCjEhBWa1w+A/z8dHOeZBj3o3AzRsa3mc24A2pb9sai8DB06nMXH2A76OOkpltBaBKOS+GtK/G3Y0r4OaiRrwiUnwUZETyK+kEbPkSNn4GZw9eWB9c35w+oGEfcPexXX1FZPORBD5YuZ9FO2IxDHNdo3B/hrSrSqe6ITg7lZz2PiLiOBRkRK5HTjbsW2LefdmzGAxzSH3cfKDBvdC0vzn2SwlqvAuQYzVYtiuOWX8cZN3B+Nz1t9YO4v9uqUrLKgEayE5EbEpBRuRqYrfBlq/NcV9ST15YHxEJTR6CeneDm5fNyisqiWlZfLfhCHPWHOJIvNmF2tXZQo/GFXjslqrUDC55d5xExDEpyIj8W8pJM7hs+Rritl1YX6YcNO4LTfpD+Zq2q68I7TuZwpy/DvHDxqOcyzTvOvmXceX+FhEMuKkSoX6eNq5QRCQvBRkRgKx0iP4VtnwF+5ZdeHTk7AY1u0Cjvua8R86utq2zCFitBiv3nGL2X4dYtedU7vpawT4MbFOZuxtXwNNNPZBExD4pyEjpZc2BQ3/A9u9hx8+QkXhhW8UW0Oh+qNcTygTYrsYidDY1k++jjvLFusMcOnMOMJv4dKwTzKCbKhNZLVDtX0TE7inISOliGHB0wz/h5SdIibuwzS/c7HHU6H4oV8N2NRYhwzDYGJPAF+sOM3/ridzu0z4eLvRpHk7/yMpEBJaxcZUiItdPQUZKPsOAuB1meNn+AyTEXNjm4Q91e5g9jyq1BaeSOQbK2dRMftp0jG83HGF3bHLu+nphvvRrXYnujcLwctc/ByLiePQvl5Rcp/fBjh9h2/dwOvrCelcvqH2nGV6qdgAXN9vVWISsVoO/9p/h6/Ux/LYjjswc8+6Lu4sT3RqF0a91JRpV9NPjIxFxaAoyUrKcioadP5uvuO0X1ju7m411G9wLNTqDW8l9fHI8IY3vo47y7YYjubNPA9Sv4Euf5uF0b1wBP8+S12hZREonBRlxbIYBsVvNCRp3/gyndl/Y5uQCVdqZ4aX2neDhZ7s6i1hKRjaLtscyd9Mx/tx/OnfkXR8PF+5pUoH7modTv0LJ/f4iUnopyIjjycmGmL/M8LJ7ASQeubDNyRWq3Wq2e6nVtcT2OALIzrGyet9p5m46xuIdsaRnWXO3ta4awP0tIuhSP0STN4pIiaYgI44hMxX2LzeDy55FkHb2wjYXT6h+mznDdM3O4OlvszKLmmEY7DiexI8bjzFvy3FOp2Tkbqtazot7mlTg7iYVCA8ouY/OREQupiAj9ivxGOz9zZzb6MDvkJ1+YVuZQKjZ1XxkVLV9iW7zAuaIu/O3Hmf+1hPsO5mSuz7Ay43ujcK4p0kFGqrhroiUQgoyYj9ysuHoejO87P0tb2NdgLKVofZdZngJbwVOJfuRyaHTqSzYdoL5W0+w60RS7np3Fyc61g2mZ5MK3FKzPK7OJbPLuIjI9VCQEdtKPQP7lprBZd9SSE+4aKPFHGG35u1Q6w4IqlviZpe+mGEY7IlLYdH2WBZuP5FnvBcXJws31yjHXQ3D6FQvGF8P9ToSEQEFGSluOdlwLMps77J/mTnKLsaF7Z5loXpHqHE7VLsNvAJtVmpxMAyDbccSWbQ9lkXbYzlwOjV3m7OThciqgdzVMJTO9UIo61Uyx7sREbkRCjJStAwDzh6EAyvM8HJgVd45jQCCG5h3XWrcDhWag3PJ/mOZlWPl74PxLNkZx5KdcRxLuDDWi5uzEzfXKEeX+iF0qhuMfxmFFxGRqynZPzHENpJj4eAqOLjSDC6JMXm3e/ibDXSr32bedfGrYIsqi1XCuUxW7jnFsl0n+T36JMnp2bnbPF2d6VC7PF3qh9KhVnl89NhIROS6KcjIjUtLgMN/woGVZni5eFA6MAemq9jCHN+l2q0Q1qTEN9Q1DINdJ5L5Pfokv+8+ycaYs1gveoIW6OXGbXWCuK1OMLfUKI+nW8n+/RARKSoKMpJ/aWfh8BozvBz6wxxZ17BetIMFQhpA1XZQpT1EtAZ3bxsVW3wSz2Xxx77TrNxzklV7ThOblJ5ne61gHzrUDqJT3WAah/vj7FRyGy6LiBQXBRm5tsRjcGQtxKw1A0zcdvI00AUIrG5OB1C1HVS+uUSPqHteZraVzUcS+GPfaVbvPcWWIwl57rp4uDrRplo5OtQOokPtICr4e9quWBGREkpBRvKyWs1HQzFrzOASs/bSNi4AgTWgchuo1Nb81Tes+GstZlarQXRcMn/uO82f+06z7mA85zJz8uxTI8ibW2qW55aa5WlVJUDTA4iIFDEFmdIu7azZHfroBnMwuqPrIf1fvYosTuajoohIcyC6Sm3AJ9g29RYjwzDYezKFNfvPsPaA+Tp7LivPPoFebtxUvRxtqgVyS83yhOmui4hIsVKQKU1ysuHkzn8Cyz/B5czeS/dzLWM2zo1obb4qtgB3n+Kvt5hl51jZHZvMuoPxrD8Yz9+H4olPzcyzj6erMy2qBHBz9XK0qV6O2iE+OKmti4iIzSjIlFRWqzl+y7GNcHwjHN8EJ7ZA1rlL9w2oaoaVCs2hYnPz7otzye8CnJqRzeYjCaw/FE/U4bNsPHyW1H89KnJ3caJ55bJEVg0kslogDSr44+aiKQFEROyFgkxJYM2B03vNoBK71fz1xNZLB54DcPeFCs3MwHI+vJTw0XPBfEx06Mw5Nh4+y6YjZ9l4OIHdsUl5GucC+Li70KxyWVpWCaBVlQAFFxERO6cg42iy0uDkLrPn0Ikt5itux+XvtLh4mHdXwppAWFPz13I1wank/2A+lZzB1qMJbDmSwKYjCWw9mkhiWtYl+1Xw96R55bI0r1SW5pUDqBnso27RIiIOREHGXhkGJMSYbVridpi/xm6DM/v+NWbLP1y9zNAS2ghCG0JIQwiqUyoeEZ1MTmfH8SS2H01k2zHzdSIx/ZL93FycqB/mS9OIsjStVJYmEf6E+qlxroiII1OQsTXDgJQ48y7LqWg4tQvidprLmcmX/0yZQAiubwaW0MZmeAmoWuJHy7VaDWLiz7HrRJIZXI4nsuN4EqeSMy7Z12KBauW9aVTRn8YR/jSu6E+tEB89JhIRKWEUZIqLNce8w3J6j/k6FW22azm1G9ITLv8ZJ1fzUVBwXQiqa95xCa4PPiHmT+oS7GxqJtFxyeyJS2bXiWR2xyYRHZt8ybgtYP5WVCnnRYMKfrmvehX88HbXH28RkZJO/9IXtnPxEH/AfAR0/nV6r/lr9qWPOwBznJayVaB8bQiqbYaWoLpQrkaJfzSUcC6TvSdT2BuXwr6TKew9mczu2OTL3mUB8/FQzWBv6oX6Ua+CL/XCfKkd4ouXQouISKmkf/0L6uSuf9qs7DeDS/w/v6advfJnnN3NofzL1zTvtOS+aoBryW2rkZ1j5ejZNA6cTuHAqVT2n0ph/6lUDpxK4XRK5hU/V7GsJ7WCfagZ4kOdUF/qhPhQpZwXLs56PCQiIiYFmYL6Yyps/eby23zCILCaGVoCq10ILP4RJbYdS1aOleMJaRw6c46YM6kcPH2OQ2dSOXQ6lSNnz5GVY1zxsxX8Pake5E2NIG+qB3lTK8SHGsE+ejQkIiLXpJ8UBRXW1JxMMbCq2dA2oCoEVIOAKuDmZevqCp1hGJxKyeDY2TSOnk0jJv4cR8+eIyb+HEfi0ziWkEbOvwdluYi7ixNVynlRrbw31cp7UbW8N1XLm8t6LCQiIgWlnyAF1fpx81VCpGXmcCIxjROJ6RxPSON4wj+/JqZx7KwZVDKyL9Pt+yLuLk5EBJShUmAZKgd6UbmcF1XKmb+G+npoKH8RESl0CjIlXHaOlTOpmZxMyuBkcjqxSenEJWUQl3j+vflrwrlLB4v7N4sFQnw9qFjWk/CyZQgP+OdV1pOIwDIE+yisiIhI8VKQcUCZ2VbOnsvkdEoGZ1IyOZOawelkc/lUcganUjI4nZLJqeQMzqRmYFz5iU8eZdycCfXzIMzfkwr+noT5exLq50EFf08qli1DiJ+HxmERERG7oiBjQ4ZhkJKRTWJalvk6l0VCWhZnz2WScC6Ls6mZnD1nLsenmq+zqZkkZ2Tn6zxOFijn7U6Qrzshvh4E+XoQ4utBsK87Qb4ehPl5EuLnga+HC5YSPj6NiIiULAoyN+B8A9iU9GxSMrJJSc8m+fyv6Vkk/7OcnJ5FUlo2SelZJJ0PLWlZJKVnX7WB7NU4O1kI8HIj0MuNct7uBHqbv5b3caectzvl/lkO8nUn0Mtd8weJiEiJ5BBB5r333uONN94gNjaWRo0a8e6779KyZUtbl0W21aDlf5fd8HHcnJ3wK+OKv6crfp6u+Jdxo2wZV8p6ueFfxpWAMm4EeOV9+Xq4qj2KiIiUenYfZL755htGjRrFjBkzaNWqFW+//TadO3cmOjqaoKAgm9bm6uxEGTdnnJ0s+Li74O3hgre7C17uLvh6uOLt7oKPhwu+nq74/vOrj4cZVi5+ebg66ZGOiIhIAVgM43qbgtpGq1ataNGiBf/73/8AsFqthIeHM3z4cJ599tlL9s/IyCAj48Lw9klJSYSHh5OYmIivr2+h12cYhkKIiIhIIUtKSsLPz++aP7/tugtKZmYmUVFRdOzYMXedk5MTHTt2ZM2aNZf9zKRJk/Dz88t9hYeHF2mNCjEiIiK2Y9dB5vTp0+Tk5BAcHJxnfXBwMLGxsZf9zNixY0lMTMx9HTlypDhKFRERERuw+zYy+eXu7o67u7utyxAREZFiYNd3ZMqVK4ezszNxcXF51sfFxRESEmKjqkRERMRe2HWQcXNzo1mzZixbdqGLs9VqZdmyZURGRtqwMhEREbEHdv9oadSoUQwYMIDmzZvTsmVL3n77bVJTUxk0aJCtSxMREREbs/sg06dPH06dOsX48eOJjY2lcePGLFq06JIGwCIiIlL62P04Mjfqevuhi4iIiP0oEePIiIiIiFyNgoyIiIg4LAUZERERcVgKMiIiIuKwFGRERETEYSnIiIiIiMOy+3FkbtT53uVJSUk2rkRERESu1/mf29caJabEB5nk5GQAwsPDbVyJiIiI5FdycjJ+fn5X3F7iB8SzWq0cP34cHx8fLBZLkZwjKSmJ8PBwjhw5okH3bEzXwn7oWtgPXQv7oWtx/QzDIDk5mbCwMJycrtwSpsTfkXFycqJixYrFci5fX1/9wbQTuhb2Q9fCfuha2A9di+tztTsx56mxr4iIiDgsBRkRERFxWAoyhcDd3Z0XX3wRd3d3W5dS6ula2A9dC/uha2E/dC0KX4lv7CsiIiIll+7IiIiIiMNSkBERERGHpSAjIiIiDktBRkRERByWgsxVrFq1im7duhEWFobFYmHu3Ll5thuGwfjx4wkNDcXT05OOHTuyd+/ePPvEx8fz4IMP4uvri7+/P4MHDyYlJaUYv0XJcLVrkZWVxTPPPEODBg3w8vIiLCyM/v37c/z48TzH0LW4cdf6O3Gxxx9/HIvFwttvv51nva5D4biea7Fr1y66d++On58fXl5etGjRgpiYmNzt6enpDB06lMDAQLy9venVqxdxcXHF+C1Khmtdi5SUFIYNG0bFihXx9PSkbt26zJgxI88+uhYFpyBzFampqTRq1Ij33nvvstsnT57MO++8w4wZM1i3bh1eXl507tyZ9PT03H0efPBBduzYwZIlS5g/fz6rVq3iscceK66vUGJc7VqcO3eOjRs3Mm7cODZu3MiPP/5IdHQ03bt3z7OfrsWNu9bfifN++ukn1q5dS1hY2CXbdB0Kx7Wuxf79+2nbti21a9dmxYoVbN26lXHjxuHh4ZG7z8iRI/nll1/47rvvWLlyJcePH6dnz57F9RVKjGtdi1GjRrFo0SI+//xzdu3axYgRIxg2bBjz5s3L3UfX4gYYcl0A46effspdtlqtRkhIiPHGG2/krktISDDc3d2Nr776yjAMw9i5c6cBGOvXr8/dZ+HChYbFYjGOHTtWbLWXNP++Fpfz999/G4Bx+PBhwzB0LYrCla7D0aNHjQoVKhjbt283KlWqZEydOjV3m65D0bjctejTp4/Rr1+/K34mISHBcHV1Nb777rvcdbt27TIAY82aNUVVaol3uWtRr149Y+LEiXnWNW3a1Hj++ecNw9C1uFG6I1NABw8eJDY2lo4dO+au8/Pzo1WrVqxZswaANWvW4O/vT/PmzXP36dixI05OTqxbt67Yay5NEhMTsVgs+Pv7A7oWxcVqtfLQQw8xevRo6tWrd8l2XYfiYbVaWbBgATVr1qRz584EBQXRqlWrPI88oqKiyMrKyvNvWO3atYmIiMj9N0wKx0033cS8efM4duwYhmHw+++/s2fPHm6//XZA1+JGKcgUUGxsLADBwcF51gcHB+dui42NJSgoKM92FxcXAgICcveRwpeens4zzzxD3759cydl07UoHq+//jouLi48+eSTl92u61A8Tp48SUpKCq+99hpdunTht99+45577qFnz56sXLkSMK+Fm5tbbtg/7+J/w6RwvPvuu9StW5eKFSvi5uZGly5deO+997jlllsAXYsbVeJnv5bSJSsri/vuuw/DMJg+fbqtyylVoqKimDZtGhs3bsRisdi6nFLNarUC0KNHD0aOHAlA48aN+euvv5gxYwbt2rWzZXmlzrvvvsvatWuZN28elSpVYtWqVQwdOpSwsLA8d2GkYHRHpoBCQkIALmlVHhcXl7stJCSEkydP5tmenZ1NfHx87j5SeM6HmMOHD7NkyZLcuzGga1EcVq9ezcmTJ4mIiMDFxQUXFxcOHz7MU089ReXKlQFdh+JSrlw5XFxcqFu3bp71derUye21FBISQmZmJgkJCXn2ufjfMLlxaWlpPPfcc7z11lt069aNhg0bMmzYMPr06cOUKVMAXYsbpSBTQFWqVCEkJIRly5blrktKSmLdunVERkYCEBkZSUJCAlFRUbn7LF++HKvVSqtWrYq95pLsfIjZu3cvS5cuJTAwMM92XYui99BDD7F161Y2b96c+woLC2P06NEsXrwY0HUoLm5ubrRo0YLo6Og86/fs2UOlSpUAaNasGa6urnn+DYuOjiYmJib33zC5cVlZWWRlZeHklPfHrbOzc+6dM12LG6NHS1eRkpLCvn37cpcPHjzI5s2bCQgIICIighEjRvDKK69Qo0YNqlSpwrhx4wgLC+Puu+8GzP/9dOnShUcffZQZM2aQlZXFsGHDuP/++y/bLVWu7GrXIjQ0lHvvvZeNGzcyf/58cnJycp8rBwQE4ObmpmtRSK71d+LfAdLV1ZWQkBBq1aoF6O9EYbrWtRg9ejR9+vThlltuoUOHDixatIhffvmFFStWAGbnhMGDBzNq1CgCAgLw9fVl+PDhREZG0rp1axt9K8d0rWvRrl07Ro8ejaenJ5UqVWLlypV8+umnvPXWW4CuxQ2zdbcpe/b7778bwCWvAQMGGIZhdsEeN26cERwcbLi7uxu33XabER0dnecYZ86cMfr27Wt4e3sbvr6+xqBBg4zk5GQbfBvHdrVrcfDgwctuA4zff/899xi6FjfuWn8n/u3f3a8NQ9ehsFzPtZg1a5ZRvXp1w8PDw2jUqJExd+7cPMdIS0sznnjiCaNs2bJGmTJljHvuucc4ceJEMX8Tx3eta3HixAlj4MCBRlhYmOHh4WHUqlXLePPNNw2r1Zp7DF2LgrMYhmEUQ14SERERKXRqIyMiIiIOS0FGREREHJaCjIiIiDgsBRkRERFxWAoyIiIi4rAUZERERMRhKciIiIiIw1KQEREREYelICMiIiIOS0FGRGzKYrFc9fXSSy9d9fMdOnTgo48+uuy29u3bM2LEiDzrpk2bhru7O19//XUhfQMRsSVNGikiNnXixInc99988w3jx4/PM2uzt7f3FT8bHx/Pn3/+ed2h5MUXX2TKlCn8/PPPdOnSpeBFi4jdUJAREZsKCQnJfe/n54fFYsmz7moWLFhA06ZNCQ4Ovup+hmHw5JNP8vnnn7NkyRJuuummG6pZROyHgoyIOKx58+bRo0ePq+6TnZ1Nv379WL58OStXrqRhw4bFVJ2IFAcFGRFxSBkZGSxatOiabWhmzpwJwJYtW6hdu3YxVCYixUmNfUXEIS1fvpygoCDq1at31f3atm2Lt7c348aNIzs7u5iqE5HioiAjIg5p3rx5dO/e/Zr7NWjQgGXLlvH777/Tp08fhRmREkZBRkQcjmEY/PLLL9dsH3Ne48aNWbZsGatWreK+++4jKyuriCsUkeKiICMiDicqKopz587Rtm3b6/5Mo0aNWL58OX/88YfCjEgJoiAjIg7n559/5o477sDFJX/9FRo0aMDy5cv566+/6N27N5mZmUVUoYgUF4thGIatixARyY+GDRvywgsvcN9999m6FBGxMd2RERGHkpmZSa9evejatautSxERO6A7MiIiIuKwdEdGREREHJaCjIiIiDgsBRkRERFxWAoyIiIi4rAUZERERMRhKciIiIiIw1KQEREREYelICMiIiIOS0FGREREHNb/A048EGFlp/lXAAAAAElFTkSuQmCC", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import yaeos\n", "\n", "import matplotlib.pyplot as plt\n", "\n", "import numpy as np\n", "\n", "tcs = np.array([190.6, 369.8]) # critical temperatures [K]\n", "pcs = np.array([45.99, 42.48]) # critical pressures [bar]\n", "w = np.array([0.0115, 0.0866]) # acentric factors [-]\n", "\n", "model_pr76 = yaeos.PengRobinson76(tcs, pcs, w)\n", "psat_pr76 = model_pr76.pure_saturation_pressures(1)\n", "\n", "# Define the alpha soave with a value of k=0 for the first component and\n", "# 10.3 for the second one. Just as example values.\n", "k = [00.000, 10.3]\n", "alphasoave = yaeos.AlphaSoave(k=k)\n", "\n", "model_pr76.set_alpha(alphasoave)\n", "psat_pr76_modified = model_pr76.pure_saturation_pressures(1)\n", "\n", "plt.plot(psat_pr76[\"T\"], psat_pr76[\"P\"], label=r\"PR76 with original $\\alpha$\")\n", "plt.plot(psat_pr76_modified[\"T\"], psat_pr76_modified[\"P\"], label=r\"PR76 with modified $\\alpha$\");\n", "plt.legend(frameon=False)\n", "\n", "plt.xlabel(\"T / K\")\n", "plt.ylabel(\"P / bar\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Alpha RKPR\n", "\n", "The RKPR EoS uses a different $\\alpha$ function. This function changes the\n", "functionality with Temperature. Being inversely proportional to the reduced\n", "temperature $T_r$, with an exponent $k$\n", "\n", "$$\n", "\\alpha = \\left(\\frac{3}{2 + T_r}\\right)^k\n", "$$" ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import yaeos\n", "\n", "import matplotlib.pyplot as plt\n", "\n", "import numpy as np\n", "\n", "k = [3.000, 10.3]\n", "alpharkpr = yaeos.AlphaRKPR(k=k)\n", "\n", "tcs = np.array([190.6, 369.8]) # critical temperatures [K]\n", "pcs = np.array([45.99, 42.48]) # critical pressures [bar]\n", "w = np.array([0.0115, 0.0866]) # acentric factors [-]\n", "\n", "model_pr76 = yaeos.PengRobinson76(tcs, pcs, w)\n", "psat_pr76 = model_pr76.pure_saturation_pressures(1)\n", "\n", "model_pr76.set_alpha(alpharkpr)\n", "psat_pr76_modified = model_pr76.pure_saturation_pressures(1)\n", "\n", "plt.plot(psat_pr76[\"T\"], psat_pr76[\"P\"], label=r\"PR76 with original $\\alpha$\")\n", "plt.plot(psat_pr76_modified[\"T\"], psat_pr76_modified[\"P\"], label=r\"PR76 with modified $\\alpha$\");\n", "plt.legend(frameon=False)\n", "plt.xlabel(\"T / K\")\n", "plt.ylabel(\"P / bar\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Alpha Mathias-Copeman\n", "The alpha function defined by Mathias and Copeman. This function consists in\n", "a piecewise function, either for temperatures above or below the critical point.\n", "Above the critical point, the same functionality as the Soave alpha is used. But,\n", "for temperatures below the critical point, a third order polinomial is used.\n", "\n", "\\begin{cases}\n", " \\alpha = (1 + c_1(1 - \\sqrt{T_r}))^2 & \\rightarrow T_r > 1\\\\\n", " \\alpha = (-c_1(\\sqrt{T_r} - 1) + c_2(\\sqrt{Tr} - 1)^2 - c_3(\\sqrt{Tr} - 1)^3 + 1)^2 & \\rightarrow T_r <= 1\n", "\\end{cases}" ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "\n", "import yaeos\n", "\n", "import matplotlib.pyplot as plt\n", "\n", "import numpy as np\n", "\n", "c1 = [5.000, 0.3]\n", "c2 = [0.000, 0.3]\n", "c3 = [0.9, 0.3]\n", "\n", "alphamc = yaeos.AlphaMathiasCopeman(c1, c2, c3)\n", "\n", "tcs = np.array([190.6, 369.8]) # critical temperatures [K]\n", "pcs = np.array([45.99, 42.48]) # critical pressures [bar]\n", "w = np.array([0.0115, 0.0866]) # acentric factors [-]\n", "\n", "model_pr76 = yaeos.PengRobinson76(tcs, pcs, w)\n", "psat_pr76 = model_pr76.pure_saturation_pressures(1)\n", "\n", "model_pr76.set_alpha(alphamc)\n", "psat_pr76_modified = model_pr76.pure_saturation_pressures(1)\n", "\n", "plt.plot(psat_pr76[\"T\"], psat_pr76[\"P\"], label=r\"PR76 with original $\\alpha$\")\n", "plt.plot(psat_pr76_modified[\"T\"], psat_pr76_modified[\"P\"], label=r\"PR76 with modified $\\alpha$\");\n", "plt.legend(frameon=False)\n", "plt.xlabel(\"T / K\")\n", "plt.ylabel(\"P / bar\");\n" ] } ], "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": "3.14.5" } }, "nbformat": 4, "nbformat_minor": 2 }