{ "cells": [ { "cell_type": "code", "execution_count": 1, "id": "d88bffed", "metadata": { "execution": { "iopub.execute_input": "2024-03-15T22:39:40.712168Z", "iopub.status.busy": "2024-03-15T22:39:40.712005Z", "iopub.status.idle": "2024-03-15T22:39:41.350923Z", "shell.execute_reply": "2024-03-15T22:39:41.350413Z" } }, "outputs": [ { "data": { "text/plain": [ "'0.19.1'" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import scipy.interpolate\n", "import teqp\n", "import numpy as np\n", "import pandas\n", "import matplotlib.pyplot as plt\n", "teqp.__version__" ] }, { "cell_type": "markdown", "id": "8218498b", "metadata": {}, "source": [ "# Critical curves & points\n", "\n", "\n", "## Pure Fluids\n", "\n", "Solving for the critical point involves finding the temperature and density that make\n", "$$\n", "\\left(\\frac{\\partial p}{\\partial \\rho}\\right)_T = \\left(\\frac{\\partial^2 p}{\\partial \\rho^2}\\right)_T = 0\n", "$$\n", "by 2D non-linear rootfinding. Newton steps are taken, and the analytic Jacobian is used (thanks to the ability to do derivatives with automatic differentiation). This is all handily wrapped up in the\n", "``solve_pure_critical`` method which requires the user to provide guess values for temperature and density" ] }, { "cell_type": "code", "execution_count": 2, "id": "46657a96", "metadata": { "execution": { "iopub.execute_input": "2024-03-15T22:39:41.353168Z", "iopub.status.busy": "2024-03-15T22:39:41.352820Z", "iopub.status.idle": "2024-03-15T22:39:41.357661Z", "shell.execute_reply": "2024-03-15T22:39:41.357148Z" } }, "outputs": [ { "data": { "text/plain": [ "(190.564, 9442.816240022832)" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Values taken from http://dx.doi.org/10.6028/jres.121.011\n", "modelPR = teqp.canonical_PR([190.564], [4599200], [0.011])\n", "\n", "# Solve for the critical point from a point close to the critical point\n", "T0 = 192.0\n", "# Critical compressibility factor of P-R is 0.307401308698.. (see https://doi.org/10.1021/acs.iecr.1c00847)\n", "rhoc = (4599200/(8.31446261815324*190.564))/0.3074\n", "rho0 = rhoc*1.2345 # Perturb to make sure we are doing something in the solver\n", "modelPR.solve_pure_critical(T0, rho0)" ] }, { "cell_type": "markdown", "id": "9141858c", "metadata": {}, "source": [ "If you have a mixture, but want to obtain the critical point of a pure fluid of this mixture, you can specify the index of the component in the mixture, as well as the number of componnts in the mixture with something like:\n", "\n", "``\n", "model.solve_pure_critical(T0, rho0, {\"alternative_pure_index\": 1, \"alternative_length\": 2})\n", "``\n", "so here, for the second fluid, with 0-based index of 1, in a two-component mixture" ] }, { "cell_type": "markdown", "id": "e15eeded", "metadata": {}, "source": [ "## Mixtures\n", "\n", "A pure fluid has a single vapor-liquid critical point, but mixtures are different:\n", "\n", "* They may have multiple (or zero!) critical points for a given mixture composition\n", "* The critical curves may not emanate from the pure fluid endpoints\n", "\n", "When it comes to critical points, intuition from pure fluids is not helpful, or sometimes even counter-productive. \n", "\n", "teqp has methods for working with the critical loci of binary mixtures (only binary mixtures, for now) and especially, methods for tracing the critical curves emanating from the pure fluid endpoints.\n", "\n", "The tracing method in teqp is based explicitly on the isochoric thermodynamics formalism introduced by Ulrich Deiters and Sergio Quinones-Cisneros. It uses the Helmholtz energy density as the fundamental potential and all other properties are derived from it. For critical curves it is based upon the integration of sets of ordinary differential equations; the differential equations are in the form of derivatives of the molar concentrations of each component in the mixture with respect to an integration variable. The set of ODE is then integrated.\n", "\n", "Here is an example of the construction of the critical curves emanating from the pure fluid endpoints for the mixture nitrogen + ethane." ] }, { "cell_type": "code", "execution_count": 3, "id": "81619ae2", "metadata": { "execution": { "iopub.execute_input": "2024-03-15T22:39:41.359808Z", "iopub.status.busy": "2024-03-15T22:39:41.359515Z", "iopub.status.idle": "2024-03-15T22:39:43.196864Z", "shell.execute_reply": "2024-03-15T22:39:43.196353Z" } }, "outputs": [ { "data": { "image/png": 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AAFpAeAZCmGmaWrR1v574aIs2llRIkrrGhOuui/vo+2MymXIOAIBWIjwDIWrDXpdmfbBZX2wvlyTFRYbpjgt76/axmYpncRMAAM4K4RkIMXsP1+gPn2zRW2uKZZpShN2m74/ppWmX9FXX2AirywMAIKgRnoEQUVFbr78u3KEXvyhQXYNHkjRpaJoemDBA6YlMNQcAQHsgPANB7miDR/9atkvPzN+mQ0ca52oenZWoh64aqKHpXawtDgCAEEN4BoLYZ1vK9P/mbvTOoNEnOVYzrxyoywZ2k2EYFlcHAEDoITwDQaigvFr/b+5GLdhcJklyxkXoZ5f3180j0xVmZxltAAA6CuEZCCKVtfV6dsF2vbikQPVuU2E2Q1MvyNS9l/VTAjNoAADQ4QjPQBDweEy9sXqPnvhoi3c57YsHJOtX12SrT3KcxdUBANB5EJ6BALduz2H96u31+nqPS5KU5YzVr64ZqEvPSbG4MgAAOh/CMxCgKmrr9YePt+gfX+2SaTYucvKTy/rqtvOzmi2nDQAA/IPwfIK8vDzl5eXJ7XZbXQo6qRJXjXbur9L2sio9+9kO7a9sbNG4blia/vvqgeoWH2VxhQAAdG6GaZqm1UUEmoqKCjkcDrlcLiUkJFhdDjqJ2SuKNOPNfJ34geztjNX/u36wLujrtKwuAACCgb/yGyPPQAAoPFClB9/Mb7LNkPT3qbnqlRRrTVEAAKAZGicBi63adVDffX5Zs+2mpL2Ha/1fEAAAOCVGngGLVNc16MmPt+jlpYVqqXnKbhjKdMb4vzAAAHBKhGfAAp9v26+Zc/K151CNJOlbI3oqOy1Bv527SW7TlN0w9NjkwUp1RFtcKQAAOBHhGfAj15F6/fb9jXp91R5JUo8u0Zo1OUfj+idLkiYO7q7C8iPKdMYQnAEACECEZ8BP5m8q1Yw5+dpfWSfDkKaMydT9EwYoNvKbj2GqI5rQDABAACM8Ax2sqq5Bv527Ua+t2C1J6p0cqyduHKKRmYkWVwYAAFqL8Ax0oOUFB/Xz19dq98EaGYb0w7FZ+vkVAxQVbre6NAAAcBYIz0AHqGtw66lPt+pvi3fKNBt7m//47aE6r3eS1aUBAIA2IDwD7WxTSYV+NnutNu+rlNQ4k8bDk7IVHxVucWUAAKCtCM9AOzFNUy9/WajHPtiso26PkmIjNGtyjq4Y1N3q0gAAQDshPAPt4FD1Ud3/xjrN21QqSRo/sJsev3GInHGRFlcGAADaE+EZaKOvdh7Qfa+t1b6KWkXYbXroqnM05fxMGYZhdWkAAKCdEZ6Bs9Tg9uiZBdv17IJt8piNU9D9zy3nalCaw+rSAABAByE8A61U4qrR6qJDen5xgdbuPiyp8abAX187qMmCJwAAIPTwLz3QCrNXFGnGm/kyjz2ODLPpiZuG6LphPSytCwAA+IfN6gKAYLH38JEmwVmS6hs8GpXFSoEAAHQWhGfAB1V1Dbpv9tdNgrMkeSQVlh+xoiQAAGAB2jaAM9heVqkf/2OVduyvbrbPbhjKdMZYUBUAALACI8/AaXy6sVTXPbtEO/ZXq3tClO6+uI/sx6agsxuGHps8WKmOaIurBAAA/sLI8wny8vKUl5cnt9ttdSmwmGmaem7RTj3x8WaZpnRe70Q9+93hcsZF6r/G9FJh+RFlOmMIzgAAdDKGaZont3F2ehUVFXI4HHK5XEpISLC6HPhZbb1bM+fk6601xZKkW8/L0COTBinczg9qAAAIVP7Kb4w8Aycoq6zVj15ZpbW7D8tuM/TrSdn6rzGZVpcFAAACBOEZOGbDXpd++PJKlbhq5YgO11++N1wX9HVaXRYAAAgghGdA0qKt+3X3P1ep+qhbvZNj9X9TcpXljLW6LAAAEGAIz+j0Xl+5WzPn5KvBY+r8Pkn6660j5IgOt7osAAAQgAjP6LRM09T/LNiupz7dKkm6flianrhpqCLCuDEQAAC0jPCMTqnB7dGv3lmvV5fvliTddXEf3X/FANlshsWVAQCAQEZ4RqdTW+/WPf9erXmbymQzpN9cO4gZNQAAgE8Iz+g0Slw12lRSobzPdmjVrkOKDLPpmVvO1YRB3a0uDQAABAnCMzqF2SuKNOPNfB1fESgizKaXpo7SmD5JltYFAACCC3dGIeSVuGqaBGdJamjwKNMZY1lNAAAgOBGeEfJWFB7UyWvQeyQVlh+xohwAABDECM8IaXsP1+jxDzc32243DEaeAQBAqxGeEbJKXDW65fmvtPdwrRJjI7zf7HbD0GOTByvVEW1pfQAAIPhwwyBC0j5XrW7521fadeCI0hOjNftHY2QYja0amc4YgjMAADgrhGeEnNKKWn33+a9UeOCIenaN1qt3nKe0Lo1hmdAMAADagrYNhJTyqjrd8vxX2llerR5dGoNzz670NgMAgPZBeEbIqKit15QXl2vn/mqlOaL02o/OU3oiwRkAALQfwjNCQm29Wz98eaU27K1QUmyE/nUHwRkAALQ/wjOCXoPbo3v+vUbLCw4qPjJML98+SlnOWKvLAgAAIYjwjKDm8Zh68M18zdtUqogwm56fMlKDezisLgsAAIQowjOC2h8/3aI3V++R3WYo77vDdV7vJKtLAgAAIYzwjKD1n5W7lffZDknSrMk5ujw7xeKKAABAqCM8Iyh9ub1cD83JlyTde2lffXtkusUVAQCAzoDwjKCzvaxSP/7nKjV4TE0amqbpl/e3uiQAANBJEJ4RVDaWuHTL88tUWdugEb266smbhsgwDKvLAgAAnQTLcyNo/HvZLj301nrv46tyuisq3G5hRQAAoLNh5BlBocRV0yQ4S9Jj729WiavGoooAAEBnRHhGUPjXV7uabXObpgrLj1hQDQAA6KwIzwh4G/dW6PnPC5pttxuGMp0swQ0AAPyH8IyA5qqp14//uVJ1DR71T4nzfsPaDUOPTR6sVEe0pfUBAIDOhRsGT5CXl6e8vDy53W6rS4Ek0zQ148112n2wRj27Rus/Px6jmnq3CsuPKNMZQ3AGAAB+Z5imaVpdRKCpqKiQw+GQy+VSQkKC1eV0Wv9atkv//dZ6hdkMvXnX+Rqa3sXqkgAAQIDyV36jbQMBacu+Sj363kZJ0gMTBxCcAQBAQCA8I+DUHHXrnn+vVl2DRxf1T9YPx/a2uiQAAABJhGcEoMc+2KRtZVVKjo/UH789VDYbKwgCAIDAQHhGQFmyvVz/ODan8x+/NVTOuEiLKwIAAPgG4RkBo7K2Xg+8sU6S9L3RGRrXP9niigAAAJoiPCNg/O79TSo+XKP0xGg9dNVAq8sBAABohvCMgLBwS5leW7FbkvTkTUMVG8kU5AAAIPCQUGCpEleNNpVU6KE5+ZKkqRdk6rzeSRZXBQAA0DLCMywze0WRZs7Jl+fYMj1dY8J1/4QB1hYFAABwGrRtwBIlrpomwVmSXEfq5aqpt64oAACAMyA8wxIF5dVNgrMkeSQVlh+xpB4AAABfEJ5hiSxnrE5e+sRuGMp0xlhSDwAAgC8Iz7BEfFR4kxk17IahxyYPVqoj2sKqAAAATo8bBmGJv3y2XVV1DUrvGq3HbshR35Q4gjMAAAh4hGf43e6DR/TCFwWSpIcnDdKFrCQIAACCBG0b8Lvff7RZRxs8Or9PksYP7GZ1OQAAAD4jPMOvvt59WHPXlcgwpF9enS3DOPm2QQAAgMBFeIZf/fHTrZKkG87toey0BIurAQAAaB3CM/xmReFBLd66X2E2Qz+9rJ/V5QAAALQa4Rl+88dPtkiSvjWyp3olxVpcDQAAQOsRnuEXX24v11c7DyrCbtM9lzLqDAAAghPhGX7xPwu2S5K+MypdPbownzMAAAhOhGd0uPmbSrV05wHZbYbuvKiP1eUAAACcNcIzOtTsFUX6wcsrJUluj6nPt+23uCIAAICzR3hGhylx1WjGm/lNtj00Z71KXDUWVQQAANA2hGd0mILyapknbXObpgrLj1hSDwAAQFsRntFhkmIjmm2zG4YynTEWVAMAANB2hGd0mCXbDzR5bDcMPTZ5sFIdzLYBAACCU5jVBSA0maapfy3bJUm6f0J/Dc9IVKYzhuAMAACCGuEZHWLpzgPasb9asRF2TTk/S3GRfKsBAIDgR9sGOsS/viqSJF1/bg+CMwAACBmEZ7S7w0eO6pON+yRJ3xvdy+JqAAAA2g/hGe3uvXUlqnebGpiaoOy0BKvLAQAAaDeEZ7S7t1bvkSRNPreHxZUAAAC0L8Iz2lVhebVWFx2WzZCuG5ZmdTkAAADtivCMdvXWmmJJ0gV9neqWEGVxNQAAAO2L8Ix2U+Kq0RurGls2rh9GywYAAAg9zCGGdjF7RZFmvJkv89jjitp6S+sBAADoCIw8o81KXDWaOeeb4CxJv527SSWuGstqAgAA6AiEZ7RZQXm1PGbTbW7TVGH5EWsKAgAA6CCEZ7RZljNWxknb7IahTGeMJfUAAAB0FMIz2izVEa3Jw7+5QdBuGHps8mClOqItrAoAAKD9ccMg2kVdg0dS48Io908cQHAGAAAhiZFntJnHY+rLHQckSd8ZlUFwBgAAIYvwjDbbWFKhg9VHFRth17kZXawuBwAAoMMQntFmn28rlySN6ZOkcDvfUgAAIHSFbNLZvXu3Lr74YmVnZ2vIkCF6/fXXrS4pZH25ozE8j+3rtLgSAACAjhWyNwyGhYXp6aef1rBhw7Rv3z6NGDFCV111lWJjY60uLaS4PabWFB2WJI3KSrK2GAAAgA4WsuE5NTVVqampkqTu3bvL6XTq4MGDhOd2trW0UlV1DYqNsGtA93irywEAAOhQAdu2sXjxYk2aNElpaWkyDENvv/12s2Py8vKUmZmpqKgojR49WsuXL2/xXKtWrZLb7VZ6enoHV935rC46JEkaltFFdtvJS6UAAACEloANz9XV1Ro6dKjy8vJa3D979mxNnz5djzzyiFavXq2hQ4dqwoQJKisra3LcwYMH9f3vf19/+9vf/FF2p/PFsZsF+6cw6gwAAEKfYZqmaXURZ2IYht566y1df/313m2jR49Wbm6unn32WUmSx+NRenq67r33Xs2YMUOSVFdXp8svv1x33HGH/uu//uuU56+rq1NdXZ33cUVFhdLT0+VyuZSQkNAxbyoEzF5RpAffzJckGZIevzFHN+dmWFsUAADolCoqKuRwODo8vwXsyPPpHD16VKtWrdL48eO922w2m8aPH6+lS5dKkkzT1G233aZLL730tMFZkmbNmiWHw+H9or3jzEpcNZpxLDhLkinpoTnrVeKqsa4oAACADhaU4bm8vFxut1spKSlNtqekpGjfvn2SpCVLlmj27Nl6++23NWzYMA0bNkz5+fktnU4zZ86Uy+Xyfu3evbvD30OwKyiv1sk/snCbpgrLj1hSDwAAgD+E7GwbY8eOlcfj8enYyMhIRUZGdnBFoSXLGStDahKg7YahTGeMVSUBAAB0uKAceXY6nbLb7SotLW2yvbS0VN27d7eoqs4l1RGt0b0TvY/thqHHJg9WqiPawqoAAAA6VlCG54iICI0YMULz58/3bvN4PJo/f77GjBljYWWdS4O7cdx52iV99cWMS7hZEAAAhLyAbduoqqrS9u3bvY8LCgq0du1aJSYmKiMjQ9OnT9eUKVM0cuRIjRo1Sk8//bSqq6s1depUC6vuXHbsr5IkXTm4OyPOAACgUwjY8Lxy5Updcskl3sfTp0+XJE2ZMkUvvfSSbr75Zu3fv18PP/yw9u3bp2HDhumjjz5qdhMhOobrSL0OHamXJGU6WbURAAB0DgEbni+++GKdaQrqe+65R/fcc4+fKsKJdh2sliQlx0cqLjJgv40AAADaVVD2PMN6hQcap6TLTGJ2DQAA0HkQnk+Ql5en7Oxs5ebmWl1KwCssbxx57pVEywYAAOg8CM8nmDZtmjZu3KgVK1ZYXUrA232wceS5VyIjzwAAoPMgPOOslFbWSZK6O6IsrgQAAMB/CM84K8WHGkeew+2GxZUAAAD4D+EZrTZ7RZF27G/sef7Z7K81e0WRxRUBAAD4B+EZrVLiqtGMN/O9j01JD81ZrxJXjXVFAQAA+AnhGa1SUF6tk2ffdpumCsuPWFIPAACAPxGe0SpZzlid3OVsNwxlOpl1AwAAhD7CM1ol1RGtH4zN8j62G4YemzxYqY5oC6sCAADwD8LzCVgkxTfDe3WVJA1IidcXMy7RzbkZFlcEAADgH4TnE7BIim8qa+slST26RjPiDAAAOhXCM1qtoqZBkpQQFWZxJQAAAP5FeEarHR95jo8Kt7gSAAAA/yI8o9Vq6t2SpJgIu8WVAAAA+BfhGa1W726c6TmMpbkBAEAnQ3hGq9W7PZKkcDvfPgAAoHMh/aDVGo6NPBOeAQBAZ0P6QatVHLth8MjRBosrAQAA8C/CM1pl9ooifbh+nyTpL5/t0OwVRRZXBAAA4D+E5xOwwuDplbhqNHNOvvexKemhOetV4qqxrigAAAA/IjyfgBUGT6+gvFoes+k2t2mqsPyINQUBAAD4GeEZPstyxsp20ux0dsNQpjPGmoIAAAD8jPAMn6U6ojVrco6O52dD0mOTByvVEW1lWQAAAH5DeEar3JyboevP7SFJ+sHYLN2cm2FxRQAAAP5DeEarOaLDJUlR4SzPDQAAOhfCM1otMqzx26a23m1xJQAAAP5FeEarxUaGSZKqWSQFAAB0MoRntFrcsfBcVcfIMwAA6FwIz2g1b3g+tkw3AABAZ0F4Rqt52zYYeQYAAJ0M4RmtFhfVGJ5LK2pZmhsAAHQqhOcT5OXlKTs7W7m5uVaXEtBWFByQJO06eEQXPL5As1cUWVwRAACAfximaZpWFxFoKioq5HA45HK5lJCQYHU5AaXEVaPzZy3Qid80dsPQFzMuYaVBAABgGX/lN0ae0SoF5dU6+X9bbtNUYfkRS+oBAADwJ8IzWiXLGSub0XSb3TCU6YyxpiAAAAA/IjyjVVId0Zo1Ocf72CbpscmDadkAAACdAuEZrXZzboYGpzX2Ev1uco5uzs2wuCIAAAD/IDzjrPTo2jjSXO/2WFwJAACA/xCecVbSujSG5+JDzPMMAAA6D8IzzkqP4+H5MOEZAAB0HoRnnJWeXQnPAACg8yE846zQtgEAADojwjPOyvG2jbLKOtU1uC2uBgAAwD8IzzgribERig63S5LWFB2yuBoAAAD/IDzjrPxn5W7V1DeOON/yt2WavaLI4ooAAAA6HuEZrVbiqtHMOfnex6akh+asV4mL/mcAABDaCM8nyMvLU3Z2tnJzc60uJaAVlFfLYzbd5jZNFZYfsaYgAAAAPyE8n2DatGnauHGjVqxYYXUpAS3LGSub0XSb3TCU6YyxpiAAAAA/ITyj1VId0Zo1OafJN89jkwcr1RFtWU0AAAD+QHjGWbk5N0Of/nyc9/Hl2d0trAYAAMA/CM84a32S45WR2NiqsbmkwuJqAAAAOh7hGW0yMDVekrSR8AwAADoBwjPaJDvVIYnwDAAAOgfCM9rk+MjzppJKiysBAADoeIRntEl2WoIkaXtZpY42eCyuBgAAoGMRntEmPbpEKyEqTPVuU9vKGH0GAAChjfCMNjEMwzv6/PaaYpboBgAAIY3wjDaLCrdLkp7/vEAXPL5As1cUWVwRAABAxwhrrxNt3LhRRUVFOnr0aJPt1157bXu9BAJQiatGi7bs9z72mNJDc9ZrXP9kVhwEAAAhp83heefOnbrhhhuUn58vwzBkmqakxh/nS5Lb7W7rSyCAFZRXyzxpm9s0VVh+hPAMAABCTpvbNn76058qKytLZWVliomJ0YYNG7R48WKNHDlSCxcubIcSEciynLGyGU232Q1Dmc4YawoCAADoQG0Oz0uXLtWjjz4qp9Mpm80mm82msWPHatasWfrJT37SHjUigKU6ojVrco6O52dD0mOTBzPqDAAAQlKbw7Pb7VZ8fONCGU6nU3v37pUk9erVS1u2bGnr6REEbs7N0E/H95MkjemTpJtzMyyuCAAAoGO0OTwPHjxYX3/9tSRp9OjReuKJJ7RkyRI9+uij6t27d5sL9Ke8vDxlZ2crNzfX6lKCzqXndJMk5Re75Pac3AUNAAAQGtocnn/5y1/K42lcWe7RRx9VQUGBLrzwQn3wwQd65pln2lygP02bNk0bN27UihUrrC4l6GSnJig+MkyVtQ3aVFJhdTkAAAAdos2zbUyYMMH7+759+2rz5s06ePCgunbt6p1xA6EvzG5TblaiFmwu01c7D2hwD4fVJQEAALS7sx559ng8+v3vf68LLrhAubm5mjFjhmpqGleXS0xMJDh3QmN6J0mSlu44YHElAAAAHeOsw/Pvfvc7PfTQQ4qLi1OPHj305z//WdOmTWvP2hBkzjsWnpcXHKTvGQAAhKSzDs+vvPKK/vKXv+jjjz/W22+/rffee0//+te/vP3P6Hyy0xIUHxWmyroGbdjrsrocAACAdnfW4bmoqEhXXXWV9/H48eNlGIZ3qjp0PnabodFZiZKkV5cXqcRVY3FFAAAA7eusw3NDQ4OioqKabAsPD1d9fX2bi0LwiomwS5JeXb5bFzy+QLNXFFlcEQAAQPs569k2TNPUbbfdpsjISO+22tpa3XnnnYqNjfVumzNnTtsqRNAocdXova9LvI89pvTQnPUa1z+ZFQcBAEBIOOvwPGXKlGbbbr311jYVg+BWUF6tk28TdJumCsuPEJ4BAEBIOOvw/Pe//70960AIyHLGymY0jjgfZzcMZTpjrCsKAACgHbV5hUHguFRHtGZNzmnyTfW7GwYx6gwAAELGWY8833777T4d9+KLL57tSyAI3ZyboVFZibriT4tV7zY1MjPR6pIAAADazVmH55deekm9evXSueeeK9NkQQx8I8sZp/N6J+nzbeWat6lMfbvFW10SAABAuzjr8HzXXXfp1VdfVUFBgaZOnapbb71ViYmMMqLRFdkp+nxbuT7esE93XtTH6nIAAADaxVn3POfl5amkpEQPPPCA3nvvPaWnp+vb3/62Pv74Y0aioSsGdZckrSk6rNKKWourAQAAaB9tumEwMjJSt9xyiz799FNt3LhRgwYN0t13363MzExVVVW1V40IQikJUTo3o4sk6ZONpdYWAwAA0E7abbYNm80mwzBkmqbcbnd7nRZBbMKx0edPNuyzuBIAAID20abwXFdXp1dffVWXX365+vfvr/z8fD377LMqKipSXFxce9WIIHU8PC/dcUCuIyzbDgAAgt9Z3zB4991367XXXlN6erpuv/12vfrqq3I6ne1ZG4JcljNW/VPitLW0Sn9dtF1Tzs9kzmcAABDUDPMs7+6z2WzKyMjQueeeK8MwTnncnDlzzro4q1RUVMjhcMjlcikhIcHqcoLaHa+s0KcbyyRJNkOaNTlHN+dmWFwVAAAINf7Kb2c98vz973//tKEZKHHVaN6x4Cw1Ltv90Jz1Gtc/mRFoAAAQlNq0SApwOgXl1Tr5xxpu01Rh+RHCMwAACErtNttGKMjLy1N2drZyc3OtLiUkZDljZTvphxN2w1CmM8aaggAAANqI8HyCadOmaePGjVqxYoXVpYSEVEe0Zk3OafJN9vMr+jPqDAAAghbhGR3q5twMLZl5qQb3cEhSszYOAACAYEJ4RodLdUTr+2N6SZLeXLWH5dsBAEDQOuvw/PDDD2vVqlXtWQtC2FU5qYqJsGtnebVW7jpkdTkAAABn5azD8549e3TllVeqZ8+euuuuu/Thhx/q6NGj7VkbQkhcZJiuGZIqSXpt+W6LqwEAADg7Zx2eX3zxRe3bt0+vvvqq4uPjdd9998npdOrGG2/UK6+8ooMHD7ZnnQgBxxdH+SC/RBW1LNcNAACCT5t6nm02my688EI98cQT2rJli5YtW6bRo0frf//3f5WWlqZx48bpD3/4g4qLi9urXgSx4Rld1LdbnGrq3Xrv671WlwMAANBq7XrD4MCBA/XAAw9oyZIl2r17t6ZMmaLPP/9cr776anu+DIKUYRi6eWS6JOk/K2jdAAAAwccwmfqgGX+tjd4ZlVfVacys+ap3m3r/J2M1KM1hdUkAACAE+Cu/MVUd/MoZF6krBnWXJL3y5S6LqwEAAGgdwjP87rbzMyVJb60t1scbSlTiqrG2IAAAAB8RnuF3I3t1VZojSkcbPPrxP1brgscXaPaKIqvLAgAAOKN2C8/FxcXMqgGf7KuoVYmr1vvYY0oPzVnPCDQAAAh4bQ7PS5YsUVZWljIyMpSRkaGUlBQ9+OCDqqioaI/6EIIKyqt18l2qbtNUYfkRS+oBAADwVZvD849//GMNHDhQK1as0JYtW/Tkk09q3rx5Gj58OCPRaFGWM1Y2o+k2u2Eo0xljTUEAAAA+avNUddHR0fr666/Vv39/7zbTNPXtb39bkvT666+3rUILMFVdx5u9okgz38yX59jjaZf00f0TzrG0JgAAELyCZqq6gQMHqqysrMk2wzD06KOP6qOPPmrr6RGibs7N0JKZl2pcP6ckaXtZlcUVAQAAnFmbw/Ntt92me++9V7t3N10xjlFbnEmqI1q/uiZbkvTJxlICNAAACHhhbT3BfffdJ0nq16+fJk+erGHDhsntduuf//ynnnjiibaeHiGuX0q8xg9M0bxNpfrb4h164qahVpcEAABwSm3ueS4tLdXatWv19ddfa+3atVq7dq22bdsmwzA0cOBA5eTkaMiQIRoyZIgmTpzYXnV3KHqe/WvVroO68a9LFW439PkDl6q7I8rqkgAAQJDxV35rc3huSW1trfLz85uE6vXr1+vw4cPt/VIdgvDsf99+bqmWFx7Ubedn6tfXDrK6HAAAEGSCOjwHO8Kz/y3ZXq7vvbBMEXabFj1wsVId0VaXBAAAgkjQzLYBtIfz+yRpdFaijro9enbBdqvLAQAAaBHhGQHBMAxNv7xxrvD/rNyt3QdZbRAAAAQewjMCxujeSRrb16l6t8noMwAACEiEZwSUnx0bfX5j9R5tL6u0uBoAAICmCM8IKCN6ddUV2Slye0w98u4GfbmjXCWuGqvLAgAAkER4RgCaceU5shnSku0H9N3nl+mCxxdo9ooiq8sCAAAgPCPwREfY5TlhAkWPKT00Zz0j0AAAwHKEZwScgvLqZtvcpqnCcmbgAAAA1iI8I+BkOWNlM5pus0nKdMZYUg8AAMBxhOcT5OXlKTs7W7m5uVaX0qmlOqI1a3JOk2/O8/smseogAACwHMtzt4DluQNDiatGb6/Zq99/tFl2m6H3fzJW53TnegAAgOZYnhudXqojWndd3EcTB3WX22Pql2+tl8fD//UAAIB1CM8IeA9PylZ0uF0rdx3Sf1butrocAADQiRGeEfDSukTrZ5f3kyT97v1N2nuYKesAAIA1CM8ICj8Y21vnZnRRZV2DZszJF636AADACoRnBAW7zdCTNw1VRJhNi7fu1+sr91hdEgAA6IQIzwgafbvF6eeX95ckPTp3o1YWHtSXO8pZeRAAAPhNmNUFAK3xwwt7a96mUq0oPKSbnlsqSbIZ0qzJObo5N8Pi6gAAQKhj5BlBxW4z9NBVA5ts85jSQ3PWMwINAAA6HOEZQaem3t1sm9s0VVh+xIJqAABAZ0J4RtDJcsbKZjTdZpOU6YyxpB4AANB5EJ4RdFId0Zo1OafJN68zPlJxkbTwAwCAjkV4RlC6OTdDS2Zeqr98b7iccREqq6zTz2Z/zfLdAACgQxGeEbRSHdG6KidVL0zJVUSYTfM2ler3H2+2uiwAABDCCM8IesPSu+jxyTmSpP9dtFMvf1lobUEAACBk0SSKkDB5eE/tPVyjP3yyVb9+b4Miwgz1SopVljNWqY5oq8sDAAAhgvCMkDHtkr7a66rVv5cVaeac9ZJYQAUAALQv2jYQMgzD0F0X926yjQVUAABAeyI8I6TsPtg8JLOACgAAaC+EZ4SUlhZQkSS36fF/MQAAIOQQnhFSji+gYjeaJui7/rlaX+08YFFVAAAgVBimabKqxEkqKirkcDjkcrmUkJBgdTk4CyWuGhWWH1HX2HD98q31WrnrkCLsNj35rSEalZWogvJqZuLopEpcNWd9/c/2uW15zY44DwCEIn/lN8JzCwjPoaW23q2fvLpGn2wsbbKdmTiC19mGyNkrijRzTr485qmvv2maqql3q7beo6MNHtW7PTrq9ui9r/fqz/O2yZRkSLp9bKbG9HaqweORaUqm9/mSeeyRaUpf7ijXa8t3e5/3vfMyNK5fssLtNoXZDdlthsLttsZfbY3bIsJsiomwKzrcrqhwuyLDbPrPyt1nrN1ff44AEIgIzxYiPIcet8fUo3M36OUvdzXZbjcMfTHjEoJDEDlVADZNU7X1Hrlq6uWqqdfhI0e9v3fV1GvPoRq91MICOv26xemo26PqOreOHG1QTb1bgfa3os1onDnmZCN6dZUzLkIJUeFKiA4/9muY93F8VJh3myM6XHGRYTKOtTT58h8JAAgm/spvzPOMTsFuMzRhUPdm4dltmtpZVk149jNfRzzrGtw6UHVUB6qOqryqTtv3V+qx9zd7R3k9pvTgm/l64qMtqqxt0FF3628M3VZWdcp9YcdGhW02qbrO3Wx/n+RYdY2JkGFIho712RuNI8yGIVXU1GtjSWWz5/XrFqeocLsaPKYa3J7GXz0eNbhN1btNHW1wq6berXq36X2fLVm161Cr3muE3abE2AjFR4dpW+k379tjSjPezJfHNNWvW7xSEqKUkhCliLDmt8UwWg2gsyM8o9M4PhPHyUFk1keb9LTjXPXtFmdNYZ3MiSOehqQfjM3SgO7x2ueqVUlFbeOvrlqVuGp0+Ei9T+c8UH3U+/swmyFHdLgc0Y2jr11iGn8fZjP05uriJs+zSXrq5qFKT4xRTESYYiPCFB1hV2ykXVFhdtmOTd1S4qrRBY8vaPK9YzcM/fOHo08bIE/1vFd+MMqn4Fnv9qi23q3CA9W69n+W6MRvXZukh6/Nlt1mU0VNvSpq61VR06CK2npV1jY023a0obH9ZF9FrfZVNH8tU/IuLnRcUmyEUhKi1N3RGKbLq2o1b2OZtwXl0esG6b/GZJ7xfRC4AYQS2jZaQNtG6Jq9okgPzVkvt2nKkBQRZlNdg0dhNkO3j83SvZf2VXxUuNVlBp2WwlFVXYN2HzzS+HWoRrsPHtG2skot2d66WU/CbIaS4iLkjItUfFSYvtp5sMl+m6S/356rvt3i5YgOV2yE3duacLITr7/dMPTY5ME+tyqc7XPb8prteZ6ao24dqK7Tweqj2l5WpZ//52ud/Jf/4B4JctXUq9RV5/MofteYcPVKilXPrtFKT4xRetcY7+/TukTp7TXFtIcA8At6ni1EeA5tx2fiyHTGyDSlX729XvM3l0mSnHGRenDiAE0e3lP2liaMhpfHY6qkolZ//6JA//dFgTeI9ewareq6Bh3ycdRYkob0cOic1Hh1d0Qr1dE40pnmiFa3+Eg5osO9I8BS20Pkidf/bGbbOJvntuU1O+I80un/HE3T1KEj9drnqlVpRa32VdRqReFBzTlp5P5MDKlZQLdJmn3neRqekXjazxij1QBai/BsIcJz5/PZ5jI9OnejCsqrJTX2pP7s8v4amu7QrgNHOs0/4CcHFtM0VV51VAXl1Sosr9bO8moVlFepsPyICg9Uq67h9KOTXWLCld41RumJ0UrvGqOE6HD94eMtTQLV2dy02Z4hsjNrzZ9jSy0oNkkvTs1Vbb1be479dGH3oRrtOXREuw/WqKa+eZ/4cRF2mzKSYtTbGaus5Fj16xavc7rHq2+3OL2zltFqAK1HeLYQ4blzqmtw6+9LCvWXz7arorahyT5D0uM3hu4/4K4j9Xr+8x3K+2yHN9j26BItV029quoaTvk8u82Qu4W72R6fnKOrh6S22ALTXm0M8L/WXDvTNLWxpELXPPNFs9HniDCbjp7iP14t3Zdgk7T4wUvUs2tM298EgJBFeLYQ4blzc9XU68/zturFJYVNthuSXv3RaJ3X22lJXb443Y+6q+saGkeQD1SrYH+1Cg40jiYXlFeftsXCMBqDdJYzVr2dscp0xirr2JfNJl30xMJmN8SdaSSZkePg1dpr11Lg/taIdO099r26c3+1duyv0tbSSm3ZV3nK78Vwu6EB3eM1OM2hwT0cyunh0IDu8YoKtzepjVYPoPMiPFuI8Iwvd5Tru88va3Hf4B4JGj8wRRf2S9bQng6F2b+Zzquj/vH25byzVxRpxpv53pkQJg7uroSocG9ILqusa/XrPnnTEE0amtYkoLT0uowk43R8DdymaWrDXpcmnTSzyKmE2Qz1S4lXTo8EHW3w6J21e2WKVg+gsyI8W4jwjJb6O6XmbQrxkWEamt5Fg3okqLK2Xq8u292qf7x9DcUnTu32s8v7aWh6V+09XHPsq1aFB6q0atfhM76vxNgIZSbFKMsZpyxn46+ZzhhFhdt0+VOLWz2CfOL7YCQZ7eXk/5D99oZBGtPbqY0lFVpf7FJ+sUvri12n/4mJpF9fm61Lz0lRz67Rp5yBBUDoIDxbiPAMqeUR1cuzu+uTDfv0+bZyfbG9XK6a088ocfnAbkrtEq0uMRHqGtO4wltEmE1hNpuW7SzXP74q8o4U3ziih4b07KKao24drqnXoeqj2nu4Rou3lZ/1e7hxeA9d2C+5sdUiKVaOmFNPw8cIMgLJmf5DZpqm9rpqlb/HpY/Wl+jttXtPea7k+EgNz+ii4RldNbxXV+X0cNDuAYQgwrOFCM847nT/gLs9pjaVVCi/2KV5m0o1f1OZ3+pKT4xRv25xSnVEKa1LtGIi7Hr0vY3MYoFOqaWfFBmSzkmN17bSKjWc9COkiDCbzk3votG9k1R7tEHPf15AuwcQAgjPFiI8o7VO9Y/3Ty7rJ49p6tCRozpU3ThzRYPHowNVR7V5X/Nlm0dlJapHl2h1iQlXYkyEbDbD56ndGDlGZ3aq7//aerfyi11aveuQVhcd0qpdh1Veder+f5uk+b+4SFlOVhwFgg3h2UKEZ5yN1oTXUy3b3NZQzMgxOjNfvv9N01ThgSP6aucBvff1Xn25o/mKl2E2Q6OyEjWuf7LG9UvWwNR4eqaBIEB4thDhGWerNeGVUAxYq8RVo/NnLTjjzB7OuEiN6+fUuP7JGtvPKWdcJH3SQAAiPFuI8Ax/IRQD1jr5P7G/u2GQcrOS9PnW/Vq8rVxLdxxotlJijy5RKj5cKyn0F1ACggnh2UKEZwDoPE73n9i6BrdW7TqkxVvLtXjrfm0sqWj2fEPSH741RFcPOf2c6AA6FuHZQoRnAEBLPsjfq7v/tabFfdHhdo3r79T4gSkaPzBFXWMj/Fwd0Ln5K7+FddiZAQAIMedmdJXNULOZdZLjI1VWWaePN5Tq4w2lCrMZOr+vU9fkpOqKQSnqEtMYpOmVBoIfI88tYOQZAHAqLd3s++2R6dqwt0LzNjWG500ntHeE2Qxd0Nep5PgIvbmqmDmlgQ5C24aFCM8AgNM5082+O/dX6YP8Er2fv69JkD6RTdKSmZcyAg20E8KzhQjPAID2smN/lZ5buEOvr9rTbN/F/ZP144v6aHRWomw25pIG2oLwbCHCMwCgPbW0MNKJenSJ1vXnpumGc3uqbzdWNwTOBuHZQoRnAEB7O7FX2ibpRxf11uEj9Xp/XYkq6xq8xw3P6KLvjMrQNUNSFRPBff2ArwjP7eCGG27QwoULddlll+mNN97w+XmEZwBAR2ipV7q23q15m0o1Z3WxFm3dL/ex4en4yDBdf24P3TIqQ9lpCd7nM1sH0DLCcztYuHChKisr9fLLLxOeAQABr6yyVm+s2qPXlu9W0cEj3u1D07uob3Ks5qxmtg7gVPyV32wdduYAcPHFFys+Pt7qMgAA8Em3+CjdfXFfLfzFxfrnD0br6pxUhdkMfb37sN48FpylxnmmH5qzXiWuGkvrBTqjgA3Pixcv1qRJk5SWlibDMPT22283OyYvL0+ZmZmKiorS6NGjtXz5cv8XCgBAO7PZDI3t51Te94Zr6czLdMuo9GbHuE1Tc78uUQj/ABkISAEbnqurqzV06FDl5eW1uH/27NmaPn26HnnkEa1evVpDhw7VhAkTVFZW5udKAQDoOMnxkfrJZf3U0kR2v/tgkyY+/bleXV6kmqNuv9cGdEYBG56vvPJK/fa3v9UNN9zQ4v6nnnpKd9xxh6ZOnars7Gw999xziomJ0Ysvvtjq16qrq1NFRUWTLwAAAkWqI1qP35gju9EYoW2SxvROVEyEXVtKKzVzTr4u+P0C/XneNh2qPmptsUCIC8o5cI4ePapVq1Zp5syZ3m02m03jx4/X0qVLW32+WbNm6Te/+U17lggAQLu6OTdD4/onN5mtw1VTr9dX7tZLXxZqz6Ea/WneVj23aIe+MypdP7ywt3p0YUYOoL0F7Mjz6ZSXl8vtdislJaXJ9pSUFO3bt8/7ePz48frWt76lDz74QD179jxlsJ45c6ZcLpf3a/fu3R1aPwAAZyPVEa0xfZK809Q5osP1wwt7a+EvLtYzt5yr7NQE1dS79fclhbroic80/T9rtbW0UiWuGn25o5wbDIF2EJQjz76aN2+eT8dFRkYqMjKyg6sBAKBjhNltunZomiYNSdXn28r114U7tHTnAc1ZXaw5q4u9xzHFHdB2QTny7HQ6ZbfbVVpa2mR7aWmpunfvblFVAABYyzAMjeufrFd/dJ7emXaBLhmQ3GS/x5RmvpnPCDTQBkEZniMiIjRixAjNnz/fu83j8Wj+/PkaM2aMhZUBABAYhqZ30R3jejfb7pF077/XaMNel/+LAkJAwLZtVFVVafv27d7HBQUFWrt2rRITE5WRkaHp06drypQpGjlypEaNGqWnn35a1dXVmjp1qoVVAwAQOLKcsbIZjSPOJ1q565CufuYLXZGdovvG9/cu/w3gzAJ2ee6FCxfqkksuabZ9ypQpeumllyRJzz77rJ588knt27dPw4YN0zPPPKPRo0e3+bVZnhsAECpmryjSQ3PWy22ashuGfjq+r7aXVeu9dXtlmpJhSNcP66Hpl/dXemKMSlw1KiivVpYz1ntjIhAM/JXfAjY8W4nwDAAIJSWumiZT3EnS9rJK/WneNr2/rkSSFGG3KTerq77cfkCmuLkQwYfwbIG8vDzl5eXJ7XZr69athGcAQMjL3+PS7z/arC+2lzfbZzcMfTHjEkagERQIzxZi5BkA0Nn876IdmvXh5mbb//WD0bqgn9OCioDW8Vd+C8rZNgAAQPu6dliajBa2P/zuen3Zwqg00FkRngEAgFId0Xr8xhzZjcYIbUiKDrdrx/5qffeFZfrRKytVWF7NaoXo9GjbaAFtGwCAzurEmwujw+16et42/eOrXXJ7TNlthtzH5r3jhkIEGnqeLUR4BgDgG9tKK/XLt9drWcHBJtttkpbMvJQbChEQ6HkGAAABoV9KvH5yWd9m2z2SFm7Z7/+CAAsRngEAwBn1To6TrYU7Cv/7rXz95r0Nqqyt939RgAUIzwAA4IxSHdGaNfmbGwptkob0dMhjSn9fUqhL/7hI76wtlmma3FSIkEbPcwvoeQYAoGUnr1b4+bb9evidDSoor5Yk9UmO1c791axSCL/jhkELsMIgAACtV9fg1t8W7dT/fLZdRxs8TfaxSiH8hfBsIUaeAQBovbfW7NHPZn/dbPurd5ynMX2SLKgInQmzbQAAgKByXu+kFlcpfH3lbm4oRMggPAMAgHbR0iqFkjRnTbEuf2qx5m0slSRuKERQo22jBbRtAABw9k68qbBgf7VmvpWvXQeOSGqcoSN/j4sbCtHu6Hm2EOEZAID2U1vv1p/mbdULiwvkPil2cEMh2gs9zwAAICREhds188qBevT6Qc32uU1TheVHLKgKODuEZwAA4BeXntOtxRsKN5W4WFwFQYO2jRbQtgEAQMeYvaJID81Z36x9Izs1QZtKKuiFxlmj59lChGcAADrO8RsKeyZG6d21JfrTp1vV4KEXGm1Dz7MF8vLylJ2drdzcXKtLAQAgZKU6ojWmT5LSu8Zq2iV99dsbBjc7hl5oBCrC8wmmTZumjRs3asWKFVaXAgBAp3FR/+QWe6ELyqv8XgtwJoRnAABgqZMXVznuobfW66evrdHW0gpuJETAoOe5BfQ8AwDgf8d7odO6ROn1lXv010U75D6hF5obCXE69DwDAIBO5XgvdK+kWP1iwgA9d+vwJvs9pjTzzXxGoGEpwjMAAAhIsZFhzbZ5JH2+tdz/xQDHNP+uBAAACABZzljZjMYR5xP98u31qj7aoCsGpWjXgSPKcsYypR38hp7nFtDzDABAYDhxURWbpH4pcdpS2nQWDnqhIbFIiqUIzwAABI7jNxJmOmPUPSFKeZ9t1x8+2drkGBZVgb/yG20bAAAgoKU6opuE4uG9ujY7xm2a2lZaRXhGh+OGQQAAEFSO90Kf7Lfvb1RBebVKXDXMC40OQ9tGC2jbAAAgsJ3cCx0VYdeRo25FhNlU3+CRKXqhOxvaNiyQl5envLw8ud1uq0sBAACncXNuhsb1T/b2QhsydNe/VmlN0WHvMR5TemjOeo3rn0w7B9oNI88tYOQZAIDg88W2/br1/5Y32/7qHedpTJ8kCyqCPzHyDAAA0Ap9usW1OC90fvFhmTKZDxrtgpHnFjDyDABAcDqxF/pkhqTHb6QHOlQx8gwAANBKJ/ZCR9ilG5/7yrvPlDTjzXzFRNg1MjORUWicFcIzAAAIKcfnhf5yR3mzfaake19dK5sh/WBslm4fm0WIRqswzzMAAAhJp5oPWmrsi37+8wKdP2uBZq8o8m9hCGqEZwAAEJJSHdGaNTlHduMUCVqNI9Ez5+SzoAp8RngGAAAh6+bcDH0x4xLlffdcnSpCe0zpfxZs82tdCF6EZwAAENJSHdG6ekiaHr8x55RtHP9etltPfrzZv4UhKBGeEdhcxVLB4sZfAQBog5tzM7RkxqW6Oqd7i/vzPtuhX7+z3s9VIdgQnhG4Vr8i/WmQ9PIk6enBjY8BAGiDVEe0fnlN9in3v7R0l/r/9wd6f12JH6tCMCE8IzDtWSW9e68ab+WQZHqk9+5jBBoA0GapjmjNvOqcU+4/6jY1/T9rVV5V58eqECwIzwg8q1+RXri0+XbTLR3c6f96AAAh58fj+mjaJX1Oub+uwaNfvP61HytCsCA8I7C4iqV3f9LyPsMuJfb2bz0AgJB1/4RzdNuYXqfcv3DLfs1dt9ePFSEYEJ5PkJeXp+zsbOXm5lpdSufkKpY++W95WzVOZNikSU9Ljh7+rgoAEMJ+fd1gJcaEn3L/A2+so30DTRimabaQVDq3iooKORwOuVwuJSQkWF1O57D6lWMjzi19O9qkH86Teo7wd1UAgBBnmqbG/n6Big/XnvKYiYO767lb+Tco0PkrvzHyDOsd3nPq4GzYpWv/THAGAHSIraVVpw3OkvTR+n3aWlrpp4oQ6MKsLgCdnGlKn/5SLQbnCY9J2dfTqgEA6DD9U+I0YVCKPt5Q2uJ+myFdMai7+qfE+7kyBCpGnmGdQ0XSqzdLG95qvs+wE5wBAB3OMAz97oYcJUS1PJ4YFxmm314/2M9VIZARnmGNlX+X/pwjbf248XH66MbALDX+ys2BAAA/ccZF6nc35LS477HJOXLGRfq5IgQy2jbgX65iqfALae59TbfvWSn94FOp/kjjdHQEZwCAH10zJFVz1+3VvE1lcntM2W2GLs9O0TVD0qwuDQGG8Az/Od2MGqa7MThnXej3sgAAON6+sXTHQlXUNig2wk67BlpE2wb8w7v4ySlmRmQBFACAxZxxkXpsco6S4yI0a/IQ2jXQIkae4R/bPtFpgzM9zgCAAHDNkDRaNXBahGd0vC+eluY90sIOm3TTi1L6KIIzAAAICoRndBxXsbTxnZaDs2GTJv1ZGnyD/+sCAAA4S4RndIzTLrct6cYXCc4AACDoEJ7R/vaskt6999T7DXtjqwYAAECQYbYNtK/Vr0gvXHrq/dwcCAAAghgjz2gfrmJp97JjrRot4eZAAAAQ/AjPaLvVr0jv/VQyPS3v5+ZAAAAQIgjPJ8jLy1NeXp7cbrfVpQQPV/Hpg7Ns0g/mST1H+LUsAACAjkDP8wmmTZumjRs3asWKFVaXEjyW/fU0I8526do/E5wBAEDIYOQZZ2/PKunL/2lhhyHd9Hf6mwEAQMghPKP1XMXSV3+Rlj7b8v7z76W/GQAAhCTCM1pnyTPSp786zQE2afSdfisHAADAn+h5hu+W/Pn0wdmwNfY406oBAABCFCPP8I2rWPr04dMcwKwaAAAg9BGecWrr50gfPihdPEMqWHzq447P40xwBgAAIY7wjJZV7Zfm3ifVuqT3p5/6uBG3S+N+QasGAADoFAjPaM40pbk/k2orTn/ciKnSpD/5pyYAAIAAQHhGcxvmSJvfO8NBNmnc/X4pBwAAIFAQntFU1f7G5bZP53iPM60aAACgkyE84xvH2zXqqk5/HLNqAACATorwjG+UbfKhXUNSREzH1wIAABCAWCQF3+g2UDpnkmQYpzjAkAZe23gcAABAJ0R4xjcMQ7rmT1JkQsv7oxzS1U/5tyYAAIAAQnhGU3HJjQG6Jdf8qXE/AABAJ0V4RnODJh9r37A3Pjbsje0agydbWxcAAIDFCM9oztu+Edf4ODKedg0AAAARnnEqccnSNU9Lsd2kSU/TrgEAACCmqsPpDJ5MqwYAAMAJGHkGAAAAfER4BgAAAHxEeD5BXl6esrOzlZuba3UpAAAACECGaZqm1UUEmoqKCjkcDrlcLiUknGLBEAAAAAQMf+U3Rp4BAAAAHxGeAQAAAB8RngEAAAAfEZ4BAAAAHxGeAQAAAB8RngEAAAAfEZ4BAAAAHxGeAQAAAB8RngEAAAAfEZ4BAAAAHxGeAQAAAB8RngEAAAAfEZ4BAAAAHxGeAQAAAB8RngEAAAAfEZ4BAAAAHxGeAQAAAB8RngEAAAAfEZ4BAAAAHxGeAQAAAB8RngEAAAAfEZ4BAAAAHxGeAQAAAB8RngEAAAAfEZ4BAAAAHxGeAQAAAB8RngEAAAAfEZ4BAAAAHxGeAQAAAB8RngEAAAAfEZ5PkJeXp+zsbOXm5lpdCgAAAAKQYZqmaXURgaaiokIOh0Mul0sJCQlWlwMAAIAz8Fd+Y+QZAAAA8BHhGQAAAPAR4RkAAADwEeEZAAAA8BHhGQAAAPAR4RkAAADwEeEZAAAA8BHhGQAAAPAR4RkAAADwEeEZAAAA8BHhGQAAAPAR4RkAAADwEeEZAAAA8BHhGQAAAPAR4RkAAADwEeEZAAAA8BHhGQAAAPAR4RkAAADwEeEZAAAA8BHhGQAAAPAR4RkAAADwEeEZAAAA8BHhGQAAAPAR4RkAAADwEeEZAAAA8BHhGQAAAPAR4RkAAADwEeEZAAAA8BHhGQAAAPAR4RkAAADwEeEZAAAA8BHhGQAAAPAR4RkAAADwEeEZAAAA8BHhGQAAAPAR4RkAAADwEeEZAAAA8BHhGQAAAPAR4RkAAADwEeEZAAAA8BHhGQAAAPAR4RkAAADwEeEZAAAA8BHhGQAAAPAR4RkAAADwEeEZAAAA8FHIhue5c+dqwIAB6tevn1544QWrywEAAEAICLO6gI7Q0NCg6dOn67PPPpPD4dCIESN0ww03KCkpyerSAAAAEMRCcuR5+fLlGjRokHr06KG4uDhdeeWV+uSTT6wuCwAAAEEuIMPz4sWLNWnSJKWlpckwDL399tvNjsnLy1NmZqaioqI0evRoLV++3Ltv79696tGjh/dxjx49VFxc7I/SAQAAEMICMjxXV1dr6NChysvLa3H/7NmzNX36dD3yyCNavXq1hg4dqgkTJqisrMzPlQIAAKAzCcie5yuvvFJXXnnlKfc/9dRTuuOOOzR16lRJ0nPPPaf3339fL774ombMmKG0tLQmI83FxcUaNWrUKc9XV1enuro672OXyyVJqqioaOtbAQAAgB8cz22maXbo6wRkeD6do0ePatWqVZo5c6Z3m81m0/jx47V06VJJ0qhRo7R+/XoVFxfL4XDoww8/1K9+9atTnnPWrFn6zW9+02x7enp6+78BAAAAdJgDBw7I4XB02PmDLjyXl5fL7XYrJSWlyfaUlBRt3rxZkhQWFqY//vGPuuSSS+TxePTAAw+cdqaNmTNnavr06d7Hhw8fVq9evVRUVNShf/gIHBUVFUpPT9fu3buVkJBgdTnwA65558M171y43p2Py+VSRkaGEhMTO/R1gi48++raa6/Vtdde69OxkZGRioyMbLbd4XDwgetkEhISuOadDNe88+Gady5c787HZuvYW/oC8obB03E6nbLb7SotLW2yvbS0VN27d7eoKgAAAHQGQReeIyIiNGLECM2fP9+7zePxaP78+RozZoyFlQEAACDUBWTbRlVVlbZv3+59XFBQoLVr1yoxMVEZGRmaPn26pkyZopEjR2rUqFF6+umnVV1d7Z19o60iIyP1yCOPtNjKgdDENe98uOadD9e8c+F6dz7+uuaG2dHzeZyFhQsX6pJLLmm2fcqUKXrppZckSc8++6yefPJJ7du3T8OGDdMzzzyj0aNH+7lSAAAAdCYBGZ4BAACAQBR0Pc8AAACAVQjPAAAAgI8IzwAAAICPOlV4Xrx4sSZNmqS0tDQZhqG33367yX7TNPXwww8rNTVV0dHRGj9+vLZt29bkmIMHD+p73/ueEhIS1KVLF/3gBz9QVVWVH98FfHWm633bbbfJMIwmXxMnTmxyDNc7uMyaNUu5ubmKj49Xt27ddP3112vLli1NjqmtrdW0adOUlJSkuLg43Xjjjc3mjS8qKtLVV1+tmJgYdevWTffff78aGhr8+VbgA1+u98UXX9zsc37nnXc2OYbrHTz++te/asiQId6FT8aMGaMPP/zQu5/Pd+g50zW34jPeqcJzdXW1hg4dqry8vBb3P/HEE3rmmWf03HPPadmyZYqNjdWECRNUW1vrPeZ73/ueNmzYoE8//VRz587V4sWL9aMf/chfbwGtcKbrLUkTJ05USUmJ9+vVV19tsp/rHVwWLVqkadOm6auvvtKnn36q+vp6XXHFFaqurvYe87Of/UzvvfeeXn/9dS1atEh79+7V5MmTvfvdbreuvvpqHT16VF9++aVefvllvfTSS3r44YeteEs4DV+utyTdcccdTT7nTzzxhHcf1zu49OzZU48//rhWrVqllStX6tJLL9V1112nDRs2SOLzHYrOdM0lCz7jZiclyXzrrbe8jz0ej9m9e3fzySef9G47fPiwGRkZab766qumaZrmxo0bTUnmihUrvMd8+OGHpmEYZnFxsd9qR+udfL1N0zSnTJliXnfddad8Dtc7+JWVlZmSzEWLFpmm2fiZDg8PN19//XXvMZs2bTIlmUuXLjVN0zQ/+OAD02azmfv27fMe89e//tVMSEgw6+rq/PsG0ConX2/TNM2LLrrI/OlPf3rK53C9g1/Xrl3NF154gc93J3L8mpumNZ/xTjXyfDoFBQXat2+fxo8f793mcDg0evRoLV26VJK0dOlSdenSRSNHjvQeM378eNlsNi1btszvNaPtFi5cqG7dumnAgAG66667dODAAe8+rnfwc7lckqTExERJ0qpVq1RfX9/kc37OOecoIyOjyec8JydHKSkp3mMmTJigioqKJiMdCDwnX+/j/vWvf8npdGrw4MGaOXOmjhw54t3H9Q5ebrdbr732mqqrqzVmzBg+353Aydf8OH9/xgNyhUEr7Nu3T5Ka/OEef3x83759+9StW7cm+8PCwpSYmOg9BsFj4sSJmjx5srKysrRjxw499NBDuvLKK7V06VLZ7Xaud5DzeDy67777dMEFF2jw4MGSGj/DERER6tKlS5NjT/6ct/T3wPF9CEwtXW9J+u53v6tevXopLS1N69at04MPPqgtW7Zozpw5krjewSg/P19jxoxRbW2t4uLi9NZbbyk7O1tr167l8x2iTnXNJWs+44RndFrf+c53vL/PycnRkCFD1KdPHy1cuFCXXXaZhZWhPUybNk3r16/XF198YXUp8INTXe8T71HIyclRamqqLrvsMu3YsUN9+vTxd5loBwMGDNDatWvlcrn0xhtvaMqUKVq0aJHVZaEDneqaZ2dnW/IZp23jmO7du0tSs7tyS0tLvfu6d++usrKyJvsbGhp08OBB7zEIXr1795bT6dT27dslcb2D2T333KO5c+fqs88+U8+ePb3bu3fvrqNHj+rw4cNNjj/5c97S3wPH9yHwnOp6t2T06NGS1ORzzvUOLhEREerbt69GjBihWbNmaejQofrzn//M5zuEneqat8Qfn3HC8zFZWVnq3r275s+f791WUVGhZcuWeftqxowZo8OHD2vVqlXeYxYsWCCPx+O9WAhee/bs0YEDB5SamiqJ6x2MTNPUPffco7feeksLFixQVlZWk/0jRoxQeHh4k8/5li1bVFRU1ORznp+f3+Q/Tp9++qkSEhK8PyZEYDjT9W7J2rVrJanJ55zrHdw8Ho/q6ur4fHcix695S/zyGT+r2wyDVGVlpblmzRpzzZo1piTzqaeeMtesWWPu2rXLNE3TfPzxx80uXbqY77zzjrlu3TrzuuuuM7OyssyamhrvOSZOnGiee+655rJly8wvvvjC7Nevn3nLLbdY9ZZwGqe73pWVleYvfvELc+nSpWZBQYE5b948c/jw4Wa/fv3M2tpa7zm43sHlrrvuMh0Oh7lw4UKzpKTE+3XkyBHvMXfeeaeZkZFhLliwwFy5cqU5ZswYc8yYMd79DQ0N5uDBg80rrrjCXLt2rfnRRx+ZycnJ5syZM614SziNM13v7du3m48++qi5cuVKs6CgwHznnXfM3r17m+PGjfOeg+sdXGbMmGEuWrTILCgoMNetW2fOmDHDNAzD/OSTT0zT5PMdik53za36jHeq8PzZZ5+Zkpp9TZkyxTTNxunqfvWrX5kpKSlmZGSkedlll5lbtmxpco4DBw6Yt9xyixkXF2cmJCSYU6dONSsrKy14NziT013vI0eOmFdccYWZnJxshoeHm7169TLvuOOOJlPZmCbXO9i0dL0lmX//+9+9x9TU1Jh333232bVrVzMmJsa84YYbzJKSkibnKSwsNK+88kozOjradDqd5s9//nOzvr7ez+8GZ3Km611UVGSOGzfOTExMNCMjI82+ffua999/v+lyuZqch+sdPG6//XazV69eZkREhJmcnGxedtll3uBsmny+Q9HprrlVn3HDNE3z7MasAQAAgM6FnmcAAADAR4RnAAAAwEeEZwAAAMBHhGcAAADAR4RnAAAAwEeEZwAAAMBHhGcAAADAR4RnAAAAwEeEZwAAAMBHhGcACEIff/yxDMM47dcnn3zS4nOnTp2qX/7yly3uu+2223T99dc32fbGG28oKipKf/zjH9v7bQBA0AmzugAAQOuNGzdOJSUl3seDBw/W3Xffrbvvvtu7LTk5udnz3G635s6dq/fff9+n13nhhRc0bdo0Pffcc5o6dWrbCweAIEd4BoAgFB0drejoaElScXGxDhw4oAsvvFDdu3c/7fO+/PJLhYeHKzc394yv8cQTT+iRRx7Ra6+9phtuuKFd6gaAYEd4BoAgt2bNGknS8OHDz3jsu+++q0mTJskwjNMe9+CDD+ovf/mL5s6dq8suu6xd6gSAUEB4BoAgt3r1aqWnpyspKemMx77zzjv605/+dNpjPvzwQ73zzjuaP3++Lr300vYqEwBCAjcMAkCQW716tU+jzps2bdLevXvPOJI8ZMgQZWZm6pFHHlFVVVV7lQkAIcHn8Hz48GH97W9/8z5euXKl7r///g4p6ri5c+dq8ODBstlsWr9+fYvHLFy4UF26dNGwYcM0bNiwM46oAECo8TU8v/vuu7r88ssVFRV12uN69OihhQsXqri4WBMnTlRlZWV7lQogCJ2cAf3BNE3deeed6tu3r0aOHKkdO3Y0O6awsFAXXHCBoqKi9OyzzzbZN336dA0ePFhDhgzRvHnzWnyNG264QV27dtVNN93UqtrOOjyPHDlSTz75ZKterLUGDBigN954Q+PGjTvtcePHj9fatWu1du1a/exnP+vQmgAgkJSXl2v37t0+hed33nlH1113nU/n7dWrlxYtWqR9+/YRoIFOzorw/P7776u8vFzbt2/Xr3/9az344IPNjklISNBTTz2ln//85022v/fee9q6davWrVunhQsXasaMGXK73c2e/9Of/lSvvPJKq2vzOTz/93//tzZu3Khhw4bp0Ucf1cKFC71J/de//rVuv/12jR07VllZWfroo4901113KTs7W7feeqv3HB9//LHGjBmjc889V7feequOHj162tfs16+fzjnnnFa/qZNVVVVp4sSJysnJUU5Ojj7++OM2nxMAAsHq1aslnflmwbKyMq1cuVLXXHONz+dOT0/XwoULVVZWpgkTJqiioqJNtQIITidnQEn6/e9/r9zcXA0ZMkR/+MMfJEkej0c//vGPdc455+jaa6/V6NGjtX79ehUWFmrIkCH69re/rYEDB2rKlClqaGg47Wu+++67+q//+i9J0tVXX60vv/xSpmk2OSYxMVGjR49WeHh4k+2bNm3SRRddJJvNpsTERCUlJWnFihXNXuPiiy9WfHx8q/88fA7Pv/vd75Sdna21a9fq4YcfbrZ/165dWrRokf75z3/qpptu0tSpU7Vhwwbt3LlTa9asUXl5uZ588kktWLBAa9asUe/evfX8889Lkn74wx9q5cqVrS7+uIULF2ro0KG69tprtX379mb7P/74YyUlJSk/P1/r1q3TmDFjzvq1ACCQrFmzRikpKUpLSzvtce+9955GjRolp9PZqvP37NlTCxcuVHl5OQEa6KROzoCffPKJ9uzZo+XLl2vNmjX64IMPtH79es2ZM0f79u3Tpk2b9Lvf/U6rVq3ynmP9+vV64IEHtGnTJtXX1+uf//ynJOnhhx/Wu+++2+w19+7dqx49ekiSDMNQ165ddeDAAZ/qHTJkiD744APV1dVp9+7dWrlypYqLi9vhT6JRu822cdVVV8lutysnJ0fx8fEaNWqUpMaJ+wsLC1VcXNwkuNbV1enqq6+W1DgJ/9kaPny4CgsLFRcXp7feeku33HJLs/9d5OTk6L777tMDDzygG264gfAMIGQ8+OCDLf4482TvvPOOrr322jMe99JLLzXb1qNHD23duvVsygMQgj755BO9//77+vzzzyVJlZWV2rp1q7744gvdfPPNMgxDOTk5GjJkiPc5x3uXJek73/mO3n33Xd12223ekez2NHHiRC1btkyjR49Wjx49NHbsWNnt9nY7f7vNthEZGdl4QpvN+/vjj91utzwej66++mpvb/KmTZu8w/xtkZCQoLi4OEmNjd9FRUXN+lr69++vtWvXatCgQZo+fXqzpnIACHVjx47VLbfcYnUZAEKAx+PRI4884s10O3bs0OTJkyXplHPIn7jdMIwzzjWflpbmHS02TVOHDh3yaTrO447X9/7776u6ulr9+vXz+bln4nN4jo+Pb9MNI2PGjNFnn32mXbt2SZIqKipUUFBw1uc7rrS01Pv7L774QsnJyc3+d7F3717FxsZqypQpuu+++7R27do2vy4ABJMHHnhA6enpVpcBIAidnAGvuOIKvfDCCzpy5IikxlkvXC6Xxo4dq//85z8yTVMbNmzQunXrvM/Ztm2b9x6N2bNna+zYsad9zWuuuUb/+Mc/JDXePDhmzJgzBu7jGhoadOjQIUnSkiVLVFdXp0GDBvn+hs/A57aNpKQkDR8+XDk5OfrWt751xhkwTpacnKznn39eN954o44ePSqbzaann35aWVlZ+uEPf6g777zTO5x/3AcffKAf/ehH2r9/v8aPH68LL7xQr7/+ut59912tXLlSjz76qP7zn//oueeeU3h4uOLi4rx/0CfKz8/XL37xC9ntdkVHR+v//u//WlU7AABAZ3VyBnz44Ye1ceNGnXfeefJ4POrSpYvefPNNTZ48WZ9++qkGDhyoAQMGaMSIEd5zDB48WL///e+1bt065ebm6rvf/a6kxp7nkSNHNmsru+aaazR37lz16dNHXbp00WuvvSapcark5557Ti+88IIOHTqknJwcVVRUyG636/HHH9eePXtUV1enCy64QJLUrVs3vfzyy97zDhs2zDuIOn78eH399deqrq5Wz5499frrr/vU2muYJ9+6CAAAALTRxRdfrGeffVZxcXG66aab2jQ5RCBhhUEAAADAR4w8AwAAAD5i5BkAAADwEeEZAAAA8BHhGQAAAPAR4RkAAADwEeEZAAAA8BHhGQAAAPAR4RkAAADwEeEZAAAA8BHhGQAAAPDR/weP1M8QokndHwAAAABJRU5ErkJggg==", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import timeit\n", "import numpy as np\n", "import matplotlib.pyplot as plt \n", "import pandas\n", "import teqp\n", "\n", "def get_critical_curve(ipure):\n", " \"\"\" Return curve as pandas DataFrame \"\"\"\n", " names = ['Nitrogen', 'Ethane']\n", " model = teqp.build_multifluid_model(names, teqp.get_datapath())\n", " T0 = model.get_Tcvec()[ipure]\n", " rho0 = np.array([1.0/model.get_vcvec()[ipure]]*2)\n", " rho0[1-ipure] = 0\n", " o = teqp.TCABOptions() \n", " o.init_dt = 1.0 # step in the arclength tracing parameter\n", " o.rel_err = 1e-8\n", " o.abs_err = 1e-5\n", " o.integration_order = 5\n", " o.calc_stability = True\n", " o.polish = True\n", " curveJSON = model.trace_critical_arclength_binary(T0, rho0, '', o)\n", " df = pandas.DataFrame(curveJSON)\n", " rhotot = df['rho0 / mol/m^3']+df['rho1 / mol/m^3']\n", " df['z0 / mole frac.'] = df['rho0 / mol/m^3']/rhotot\n", " return df\n", "\n", "fig, ax = plt.subplots(1,1,figsize=(7, 6))\n", "tic = timeit.default_timer()\n", "for ipure in [1,0]:\n", " df = get_critical_curve(ipure)\n", " first_unstable = np.argmax(~df['locally stable'])\n", " df = df.iloc[0:(first_unstable if first_unstable else len(df))]\n", " line, = plt.plot(df['T / K'], df['p / Pa']/1e6, '.')\n", " \n", " # And interpolate to smooth out the curve using the arclength\n", " # parameter (which must be monotonically increasing) as \n", " # the interpolation variable\n", " tinterp = np.linspace(df['t'].min(), df['t'].max(), 10000)\n", " Tinterp = scipy.interpolate.interp1d(df['t'], df['T / K'], kind='cubic')(tinterp)\n", " pinterp = scipy.interpolate.interp1d(df['t'], df['p / Pa'], kind='cubic')(tinterp)\n", " plt.plot(Tinterp, pinterp/1e6, color=line.get_color())\n", " \n", " plt.plot(df['T / K'].iloc[0], df['p / Pa'].iloc[0]/1e6, 'd', \n", " color=line.get_color())\n", "\n", "elap = timeit.default_timer()-tic\n", "plt.gca().set(xlabel='$T$ / K', ylabel='$p$ / MPa',\n", " xlim=(100, 350), ylim=(1, 1e3))\n", "plt.yscale('log')\n", "plt.tight_layout(pad=0.2)\n", "plt.gcf().text(0,0,f'time: {elap:0.1f} s', ha='left', va='bottom', fontsize=7)\n", "plt.gcf().text(1,0,f'teqp: {teqp.__version__}', ha='right', va='bottom', fontsize=7);" ] }, { "cell_type": "markdown", "id": "6120531f", "metadata": {}, "source": [ "And now for something a bit more interesting: ethane + alkane critical curves" ] }, { "cell_type": "code", "execution_count": 4, "id": "92020440", "metadata": { "execution": { "iopub.execute_input": "2024-03-15T22:39:43.199144Z", "iopub.status.busy": "2024-03-15T22:39:43.198819Z", "iopub.status.idle": "2024-03-15T22:39:44.098196Z", "shell.execute_reply": "2024-03-15T22:39:44.097637Z" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import timeit\n", "import numpy as np\n", "import matplotlib.pyplot as plt \n", "import pandas\n", "import teqp\n", "\n", "def get_critical_curve(names, ipure):\n", " \"\"\" Return curve as pandas DataFrame \"\"\"\n", " model = teqp.build_multifluid_model(names, teqp.get_datapath())\n", " T0 = model.get_Tcvec()[ipure]\n", " rho0 = np.array([1.0/model.get_vcvec()[ipure]]*2)\n", " rho0[1-ipure] = 0\n", " o = teqp.TCABOptions() \n", "# print(dir(o))\n", " o.init_dt = 1.0 # step in the parameter\n", " o.rel_err = 1e-6 # relative error on the step\n", " o.abs_err = 1e-6 # absolute error on the step\n", " o.max_dt = 100 # cap the size of the allowed step\n", " o.calc_stability = True\n", " o.polish = True\n", " curveJSON = model.trace_critical_arclength_binary(T0, rho0, '', o)\n", " df = pandas.DataFrame(curveJSON)\n", " rhotot = df['rho0 / mol/m^3']+df['rho1 / mol/m^3']\n", " df['z0 / mole frac.'] = df['rho0 / mol/m^3']/rhotot\n", " return df\n", "\n", "fig, ax = plt.subplots(1,1,figsize=(7, 6))\n", "tic = timeit.default_timer()\n", "name0 = 'ETHANE'\n", "for othername in ['METHANE','PROPANE','BUTANE','PENTANE','HEXANE']:\n", " for ipure in [1]:\n", " df = get_critical_curve([name0, othername], ipure)\n", " line, = plt.plot(df['T / K'], df['p / Pa']/1e6, '-')\n", " plt.plot(df['T / K'].iloc[0], df['p / Pa'].iloc[0]/1e6, 'd', \n", " color=line.get_color())\n", "\n", "elap = timeit.default_timer()-tic\n", "plt.gca().set(xlabel='$T$ / K', ylabel='$p$ / MPa')#,xlim=(100, 350), ylim=(1, 1e3))\n", "plt.tight_layout(pad=0.2)\n", "plt.gcf().text(0,0,f'time: {elap:0.1f} s', ha='left', va='bottom', fontsize=7)\n", "plt.gcf().text(1,0,f'teqp: {teqp.__version__}', ha='right', va='bottom', fontsize=7);" ] }, { "cell_type": "markdown", "id": "b664c012", "metadata": {}, "source": [ "## Pure fluid EOS with nonanalytic terms\n", "\n", "For the highest accuracy EOS for normal water and carbon dioxide, there are non-analytic terms that prevent the initialization of the critical tracing at the pure fluid critical point. Instead, one can start close to, but not *AT*, the pure fluid endpoint. After deciding on that starting composition, one solves for the critical point and then traces away from it.\n", "\n", "You might need to either do tracing in two parts, one with init_c=+1 and then init_c=-1, or one tracing might be good enough.\n", "\n", "Here is an example:" ] }, { "cell_type": "code", "execution_count": 5, "id": "afe71d81", "metadata": { "execution": { "iopub.execute_input": "2024-03-15T22:39:44.100530Z", "iopub.status.busy": "2024-03-15T22:39:44.100099Z", "iopub.status.idle": "2024-03-15T22:39:46.396915Z", "shell.execute_reply": "2024-03-15T22:39:46.396347Z" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def get_critical_curve_composition(names, T0, rhovec0, init_c=-1):\n", " \"\"\" Trace the critical curve from a fixed point along it \"\"\"\n", " o = teqp.TCABOptions() \n", "# print(dir(o))\n", " o.init_dt = 1.0 # step in the parameter\n", " o.rel_err = 1e-6 # relative error on the step\n", " o.abs_err = 1e-6 # absolute error on the step\n", " o.max_dt = 100 # cap the size of the allowed step\n", " o.calc_stability = True\n", " o.polish = True\n", " o.init_c = init_c # You might need to swap the initial tracing direction by making this +1.0\n", " curveJSON = model.trace_critical_arclength_binary(T0, rhovec0, '', o)\n", " df = pandas.DataFrame(curveJSON)\n", " rhotot = df['rho0 / mol/m^3']+df['rho1 / mol/m^3']\n", " df['z0 / mole frac.'] = df['rho0 / mol/m^3']/rhotot\n", " return df\n", "\n", "# Tracing with multi-fluid from an endpoint with non-analytic terms\n", "model = teqp.build_multifluid_model([\"Water\", \"Methane\"], teqp.get_datapath())\n", "\n", "x0 = 1-1e-6 # ever so slightly away from the pure fluid\n", "molefrac = np.array([x0, 1-x0])\n", "\n", "# Solve for the actual critical point at this mole fraction with scipy\n", "y0 = [model.get_Tcvec()[0], 1/model.get_vcvec()[0]]\n", "residual = lambda y: model.get_criticality_conditions(y[0], y[1]*molefrac)\n", "res = scipy.optimize.fsolve(residual, y0)\n", "T = res[0]\n", "rho0 = res[1]\n", "rhovec0 = rho0*molefrac\n", "\n", "# Now trace from this point\n", "curve = get_critical_curve_composition(model, T0=T, rhovec0=rhovec0)\n", "plt.plot(curve['T / K'], curve['p / Pa']/1e6, label='multifluid')\n", "\n", "# With GERG-2008, things are much more straightforward...\n", "model = teqp.make_model({'kind': 'GERG2008resid', 'model': {'names': ['water','methane']}})\n", "\n", "def get_critical_curve_simple(model, ipure, T0, rho0):\n", " \"\"\" Trace from a pure fluid... \"\"\"\n", " rhovec0 = np.array([0, 0])\n", " rhovec0[ipure] = rho0\n", " o = teqp.TCABOptions()\n", " o.init_dt = 1.0 # step in the arclength tracing parameter\n", " o.rel_err = 1e-8\n", " o.abs_err = 1e-5\n", " o.integration_order = 5\n", " o.calc_stability = True\n", " o.polish = True\n", " curveJSON = model.trace_critical_arclength_binary(T0, rhovec0, '', o)\n", " df = pandas.DataFrame(curveJSON)\n", " rhotot = df['rho0 / mol/m^3']+df['rho1 / mol/m^3']\n", " df['z0 / mole frac.'] = df['rho0 / mol/m^3']/rhotot\n", " return df\n", "\n", "for ifluid in [0]:\n", " Tci = model.get_Tcvec()[ifluid]\n", " vci = model.get_vcvec()[ifluid]\n", " df = get_critical_curve_simple(model, ipure=ifluid, T0=Tci, rho0 = 1.0/vci)\n", " plt.plot(df['T / K'], df['p / Pa']/1e6, label='GERG-2008')\n", "\n", "plt.gca().set(xlabel='$T$ / K', ylabel='$p$ / MPa')\n", "plt.yscale('log')\n", "plt.xlim(600, 950)\n", "plt.ylim(20, 300)\n", "plt.legend(loc='best');" ] } ], "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": "3.11.0" } }, "nbformat": 4, "nbformat_minor": 5 }