{ "cells": [ { "cell_type": "code", "execution_count": 1, "id": "d88bffed", "metadata": { "execution": { "iopub.execute_input": "2025-10-15T23:08:09.386271Z", "iopub.status.busy": "2025-10-15T23:08:09.386122Z", "iopub.status.idle": "2025-10-15T23:08:10.046432Z", "shell.execute_reply": "2025-10-15T23:08:10.045971Z" } }, "outputs": [ { "data": { "text/plain": [ "'0.23.1'" ] }, "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": "2025-10-15T23:08:10.047940Z", "iopub.status.busy": "2025-10-15T23:08:10.047644Z", "iopub.status.idle": "2025-10-15T23:08:10.051796Z", "shell.execute_reply": "2025-10-15T23:08:10.051170Z" } }, "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": "2025-10-15T23:08:10.053021Z", "iopub.status.busy": "2025-10-15T23:08:10.052900Z", "iopub.status.idle": "2025-10-15T23:08:11.393766Z", "shell.execute_reply": "2025-10-15T23:08:11.393068Z" } }, "outputs": [ { "data": { "image/png": "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", "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": "2025-10-15T23:08:11.395131Z", "iopub.status.busy": "2025-10-15T23:08:11.394989Z", "iopub.status.idle": "2025-10-15T23:08:12.008934Z", "shell.execute_reply": "2025-10-15T23:08:12.008420Z" } }, "outputs": [ { "data": { "image/png": "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", "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(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": "2025-10-15T23:08:12.010460Z", "iopub.status.busy": "2025-10-15T23:08:12.010315Z", "iopub.status.idle": "2025-10-15T23:08:13.671885Z", "shell.execute_reply": "2025-10-15T23:08:13.671114Z" } }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAkoAAAGxCAYAAACdnpneAAAAOnRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjEwLjcsIGh0dHBzOi8vbWF0cGxvdGxpYi5vcmcvTLEjVAAAAAlwSFlzAAAPYQAAD2EBqD+naQAAUTFJREFUeJzt3Xd8VFX+//HXnUnvpAdIgNB7FxELClLE3lbXArKroqzKqohdV1dU3P3q/hR13VXURZGFRRCULqAU6T30GghJIJDeZ+7vj4HECKEm3MzM+/l45JHMvXfufOZwnXl77rnnGqZpmoiIiIjISWxWFyAiIiJSVykoiYiIiFRDQUlERESkGgpKIiIiItVQUBIRERGphoKSiIiISDUUlERERESq4WN1AXWF0+kkLS2N0NBQDMOwuhwRERE5C6ZpkpeXR/369bHZar7/x+uD0tixYxk7diylpaXs2rXL6nJERETkPKSmptKwYcMa36+hmbldcnJyiIiIIDU1lbCwMKvLERGRGna0oJTFOw7z0/bDLNl1hLxiR8U6u82gc2IEV7WM5soWMSRHh5z+7IJpwuGtsOcn2Psz7F8O5UVVt4lqAU2uhCZXQGIP8A+ppXfm3XJzc0lMTCQ7O5vw8PAa37/X9yidcOI/iLCwMAUlEREPsetwPvNSMpi3JYPV+47hrOga8Ceqni9Xt4zl6laxXNkihvBA39PvLC8ddi+EXT+6fudnVK6zA2Fx0PRqSL4akntDWEJtvCWpRm0Nm1FQEhERj1HucLJ63zHmbclg3pZM9hwpqLK+VXwofVrHck2rODolRmC3nebLtbQA9i2FXQtg9wLITKm63icQGl1WGY7i2oLGuHocBSUREXFrecVl/LT9CPO2ZLBgWybZhWUV63ztBj2bRtO3dSx9WsfRICKw+h05HXBo3fFgtBBSl4Oj9FcbGJDQsTIYJfYA34DaeltSRygoiYiI2zlwrJD5WzKZtyWDX3ZnUeaoHG4bEeTLNS1j6dsmjiuaRxMacJpTasf2VvYY7V4ExdlV14cnQdPermDU5CoIjqqNtyN1mILSOXI4HJSVlZ15Q/Eovr6+2O12q8sQ8VqmabI1PY85mzOYk5LO5rTcKuuTo4Pp2yaOvq3j6JIUgY+9msvEi7JdA7B3L3AFpGN7qq73D3MNwE7uDU2vgchknU7zcgpKZ8k0TdLT08nOzra6FLFIREQE8fHxmmdL5CJxOE1W7T3KnBRXOEo9WnlVmc2Aro3qcW2bOPq0jqNpTDVXlJWXwoGVlcEobQ2Yzsr1Nh9o2N3VY9T0aqjfBez6apRKOhrO0omQFBsbS1BQkL4svYhpmhQWFpKZmQlAQoKuZBGpLcVlDhbvOMKclHTmbcnkaEHlGCF/HxtXNI+hX9s4+rSKJSrE/+QdmCYc3lYZjPYtgdL8qttENXf1FjW9Ghr1ggBd6SzVU1A6Cw6HoyIkRUXp/LQ3Cgx0DQDNzMwkNjZWp+FEalBOYRnzt2YwZ3MGi7Yfpqiscn6j8EBf+rSKpV/bOK5sEUOQ3ym+tvIzj1+2f3wQdl5a1fVBUa5TaSd6jcJrflJC8VwKSmfhxJikoKAgiysRK5349y8rK1NQErlAh/NKmJOSzqxN6SzblUV55QRH1A8PoF/bePq1iaN7k0h8fzveqKzIddn+7gWwayFkbKy63u4PjXpWBqO49lALt7YQ76CgdA50us276d9f5MIczC5i9iZXOFq57yi/vi9Ei7gQ+reNp1+beNo1CDv5v7f8TNg+G7bNdE34+NtZsOPbVwajpJ7ge5ppAETOgYKSiIjUmt2H85m12RWONhzIqbKuY8Nw+reLZ0DbeJJ/Oxj7xFijbT+4wtGBlcCvklVo/cpxRk2ugpCY2n8z4pUUlEREpMaYpsm2jDxmbnSFo20ZeRXrDAO6N4pkQLt4+reLP3nyR0c57F/mCkbbfjj50v2ETtDyOmg50NWDpF5euQgUlOScvfrqq0ydOpV169ZVu83evXtp0qQJa9eupVOnTgAsWbKEYcOGsXXrVgYNGsSIESO4+uqrOXbsGBEREWf12kOGDCE7O5upU6dWu03v3r3p1KkT77333lm/JxG5MDsy8pi+4RDfb0hj1+HK24b42Ax6No1iQDvXabWY0N9cqVacCzvnucLRjjlVJ3y0+7l6i1oOhBYDILzBxXkzIr+ioCQX7FThJTExkUOHDhEdHV2x7Mknn6RTp07MnDmTkJCQ0wat6vzjH//A/PXABhGxzM7MfL7fcIjvN6axPaPyEnw/u40rW0QzoF0CfVvHEhHkV/WJ2fth2yxXr9HexeD81SS+gZGuUNRyoOu0mn/oRXo3IqemoCS1wm63Ex8fX2XZrl27GDZsGA0bnv+lueHh4RdamohcgN2HT4SjQ2xNrzyt5ms3uLJ5DIM6JNC3TRxhv75tiNPpuofatpmun99epRbV3BWMWl4HiZeATVeVSt2hoHSeTNOsMtfHxRToaz/rK7B69+5N+/btsdvtfPHFF/j5+fHXv/6V3//+9/zpT39i8uTJxMXF8f777zNw4EA+//xzRowYUWUG8qlTp3LLLbecsifn1Vdf5YsvvgAqrwpbsGABjRs3rjj1FhERQZMmTQAYOnQoQ4cOZdy4cTRu3Pikff32lN57773He++9x969e4GTe68KCgp45JFHmDJlCqGhoTz99NNn1S4icvb2Hing+42H+H7DIVIOVd46xMdmcEXzaAZ1qM+1beIID/xVOCordt0qZNsPsH0W5B2qXGfYIPHS4+FoIEQ3v4jvRuTcKCidp6IyB21enm3Ja6e81v/Uk65V44svvuCZZ55hxYoVTJw4kUceeYRvv/2WW265heeff553332X++67j/37959zLU8//TRbtmwhNzeXcePGARAZGUlaWuWEbydOw7Vs2ZLXXnuN3/3ud4SHh7N8+fJzfr3fGjlyJIsWLWLatGnExsby/PPPs2bNmopxUSJyflKPFjLj+Gm1TQcrw5HdZtCrWTTXd0igX5u4qqfVCo4cv4T/B9fkj2WVY5XwDYZmfVy9Rs376eay4jYUlLxAx44defHFFwF47rnneOutt4iOjubBBx8E4OWXX+ajjz5iw4YN57zvkJAQAgMDKSkpOelU2wknTsMZhkF4eHi1252r/Px8Pv30U8aPH0+fPn0AVyi8kFN7It7swLFCfjjec7T+V5fy220GlzWNYlD7BPq3jade8PFwZJpweHvlJfypyznpEv4Tp9QaXw6+ARf3DYnUAAWl8xToayfltf6Wvfa56NChQ8XfdrudqKgo2rdvX7EsLi4OoOJeZu5i165dlJaW0qNHj4plkZGRtGzZ0sKqRNxLWnYRP2w8xIwNh1iXml2x3GbApclRXN+hPv3bxlXeV81RDnuXVIajo7uq7jC+gysYtbrO9bcu4Rc3p6B0ngzDOKfTX1by9fWt8tgwjCrLTowtcjqd2Gy2k8YinbiFS22z8rVFvMmR/BJmrE9j+oZDrN53rGK5YUCPJpEM6lCfAW1/dSl/SR5sPj4Qe8dsKKp8jusS/it/dQm/enTFs7jHN71cNDExMeTl5VFQUEBwcDDAGS/j9/Pzw+G48IHtMTExpKenY5pmRXg73Ws3bdoUX19fli9fTlJSEgDHjh1j+/btXHXVVRdcj4gnKSwtZ87mDKauO8jPO47gOH5vtROTQF7fMYEB7eKJDT1+eiznAKw4Ho72/gyO0sqdBdb71SX81+gSfvFoCkpSRY8ePQgKCuL555/n8ccfZ/ny5Xz++eenfU7jxo2ZPXs227ZtIyoq6rwv4e/duzeHDx9mzJgx3H777cyaNYuZM2cSFhZ2yu1DQkL4wx/+wMiRI4mKiiI2NpYXXngBm25+KQJAucPJzzuPMG3tQWZvzqhypW7HhuHc2KkBg9onEB8e4BpvdGg9rDo+K3b6b8YsRjZ1nU5reR00vATs+voQ76AjXaqIjIxk/PjxjBw5kn/961/06dOHV199lYceeqja5zz44IMsXLiQbt26kZ+fXzE9wLlq3bo1H374IaNHj+b111/ntttu4+mnn+aTTz6p9jnvvPMO+fn53HDDDYSGhvLUU0+Rk5NT7fYins40TdalZjNtXRrT16eRVVDZE9QoKoibOjXg5k71XfdWczpdA7AX/w+2fg95lVerui7h71E5GFuX8IuXMkxNcwxAbm4u4eHh5OTknNSDUVxczJ49e2jSpAkBAbpqw1vpOJC6bM+RAqauPci0dQfZm1VYsTwq2I/rOyRwc+cGdEqMwABIWwub/gebv4Xcg5U78Q2GZtf86hL+6JNeR6SuOd33d01Qj5KIiJs6nFfCjA1pTF17sMrl/IG+dvq1jePmzg24vFk0vnYbZG6BHz9wBaRf32zWPwxa3wBtbnYNytYl/CJVKCiJiLiRgpJy5qSk8+3aNJbsrByUbT8+S/bNnRpwbZs4gv19IGsXLPkCNk2BzJTKnfgGuU6ptbsNmvZROBI5DQUlEZE6rszhZPGOI0xdd5A5vxmU3Skxgps71ef6jvWJDvGHnIOw+mPYNNl1iu0Eux80uxba3eoKSX7BFrwTEfejoCQiUkdtz8hj0qpUvl2bxpH8korlTaKDualTfW7q1IAm0cGQfxhSvnT1HO1fWrkDww7JV0G726HVIAiMuPhvQsTNKSiJiNQhOYVlfLf+IJNXH6gy7ig6xI/rO9Tn5s4N6NgwHKM4B7Z+Cz9Mhj2LwHRW7qRRL1fPUeubICTGgnch4jkUlERELOZwmvy84zCTVx9gTkoGpeWu0ONjM7imVSx3dEukd8sYfMsLYfss1+X8O+dVnQSyfhfXmKO2t0B4A4veiYjnUVASEbHI7sP5TF59gClrDpKeW1yxvFV8KHd0S+TmTvWJ8jddoWjK/1whqazy0n9i27p6jtrdCpHJFrwDEc+noCQichHlFZfx/YZDTFp9oMp91iKCfLm5UwNu79qQtnGBGHt+grljYOsMKMmt3EFksqvnqN1tENvagncg4l0UlEREapnTafLL7iwmrz7AD5sOUVzmOrVmM+CqFjHc0S2RPi2j8E9bAWv+BSnToOho5Q7CGhzvOboNEjq5btAmIheFborlBdLT03niiSdo1qwZAQEBxMXF0atXLz766CMKC13d+I0bN8YwjJN+3nrrLQD27t1bZXlkZCRXXXUVP//880mvl5uby0svvUTbtm0JDAwkKiqK7t27M2bMGI4dO3bS9iccPXqUxx57jJYtWxIYGEhSUhKPP/74Sbck2b9/P4MGDSIoKIjY2FhGjhxJeXl5lW0WLlxIly5d8Pf3p1mzZifdr87hcPDSSy/RpEkTAgMDadq0Ka+//jqaqF5qUurRQt6du50r31nA7/+9nClrD1Jc5qRpTDDPDmzFL89ew7hrbVx38P/h/34H+HwQrB7nCknBMdD9QXhgFozYBP3+CvU7KySJXGTqUfJwu3fvplevXkRERDB69Gjat2+Pv78/Gzdu5JNPPqFBgwbceOONALz22ms8+OCDVZ4fGlr1ruDz5s2jbdu2HDlyhDfeeIPrr7+e7du3ExcXB7jCzuWXX05ubi6vv/46Xbt2JTw8nG3btjFu3Di+/vprhg8ffspa09LSSEtL429/+xtt2rRh3759DBs2jLS0NCZPngy4As6gQYOIj49n6dKlHDp0iPvvvx9fX19Gjx4NwJ49exg0aBDDhg3jq6++Yv78+fzxj38kISGB/v37A/D222/z0Ucf8cUXX9C2bVtWrVrFAw88QHh4OI8//njN/QOI1ykpdzBrUzrfrEhl2e6siuWh/j7c0Kk+d3RpQCf/gxibxsO4/0H2vsonB4RD6xtdPUeNr9CNZ0XqAN3r7ThPvdfbgAED2Lx5M1u3biU4+OQJ5kzTxDAMGjduzIgRIxgxYsQp97N3716aNGnC2rVr6dSpEwAbN26kQ4cOTJs2rSJsDRs2jPHjx7N9+3bq169f7eudrUmTJnHvvfdSUFCAj48PM2fO5PrrryctLa0inH388ceMGjWKw4cP4+fnx6hRo/j+++/ZtGlTxX7uuususrOzmTVrFgDXX389cXFxfPrppxXb3HbbbQQGBjJ+/PhT1uLOx4HUvt2H85mwYj+TVx/gWGEZ4Or86dU0mju6NWRAfD7+W6e6biFyZFvlE32DodV1x2fJvgZ8/K15AyJuSvd6q6tMs+rVJxeTb9BZdb9nZWUxZ84cRo8efcqQBJxTaPm1oqIivvzySwD8/PwAcDqdTJw4kXvvvfeUIel8Xu/Ege/j4zpUly1bRvv27StCEkD//v155JFH2Lx5M507d2bZsmX07du3yn769+9fJQRedtllfPLJJ2zfvp0WLVqwfv16Fi9ezP/93/+dU33i3U70Hk1YsZ9fdleOKYoPC+B33RO5u6VBfOoPsPx/cGh95RPt/tCinyscNe8PfkEWVC8iZ0NB6XyVFcLoU4eBWvd82lndfmDnzp2YpknLli2rLI+Ojqa42HUp8vDhw3n77bcBGDVqFC+++GKVbWfOnMkVV1xR8fiyyy7DZrNRWFiIaZp07dqVPn36AHD48GGys7NPer2uXbuybZvr/6BvuOEGJkyYcFZv88iRI7z++us89NBDFcvS09OrhCSg4nF6evppt8nNzaWoqIjAwECeffZZcnNzadWqFXa7HYfDwRtvvME999xzVrWJd9t9OJ9vVqYyefUBjha45jKyGXB1y1ju7RzJlaU/Yd/wNixZXvkkmw8kX+0KR60GQUDN/5+viNQ8BSUvtGLFCpxOJ/fccw8lJZW3RRg5ciRDhgypsm2DBlUnrps4cSKtWrVi06ZNPPPMM3z++ef4+vqe9vW+/fZbSktLGTVqFEVFRQCMHj26YkwRQEpKCklJSRWPc3NzGTRoEG3atOHVV189z3davf/+97989dVXfP3117Rt25Z169YxYsQI6tevz+DBg2v89cT9lZQ7mL05g6+X7zu596hbQ+5JPEzs9i9gxhQoKzi+1oDGl7vCUesbITjKmuJF5LwpKJ0v3yBXz45Vr30WmjVrhmEYFb05JyQnuyamCwwMrLI8OjqaZs2anXafiYmJNG/enObNm1NeXs4tt9zCpk2b8Pf3JyYmhoiIiJNe70QACg0NJTs7G3CNZbrzzjsrtvn1qbq8vDwGDBhAaGgo3377bZUgFh8fz4oVK6rsPyMjo2Ldid8nlv16m7CwsIr3PHLkSJ599lnuuusuANq3b8++fft48803FZSkitP1Ht3fMZTLi+ZjX/sCLN1S+aToFtD5Pmh/B4QlWFS5iNQEBaXzZRh1/u7bUVFRXHvttXzwwQc89thj1Y5TOl+33347L7/8Mh9++CF//vOfsdls3HnnnYwfP56XX3652nFKAJGRkURGRp60PDc3l/79++Pv789333130qDpnj178sYbb5CZmUlsbCwAc+fOJSwsjDZt2lRs88MPP1R53ty5c+nZs2fF48LCQmy2qrNj2O12nE4nIqfvPWrAffH7id7+EcyYXnkbEZ9A1+1DutwPSZfqMn4RD6Gg5OE+/PBDevXqRbdu3Xj11Vfp0KEDNpuNlStXsnXrVrp27VqxbV5eXsU4nxOCgoKqvYrAMAwef/xxXn31VR5++GGCgoIYPXo0Cxcu5JJLLuG1116jW7duBAcHs2HDBpYtW0a7du2qrTU3N5d+/fpRWFjI+PHjyc3NJTfXNSNxTEwMdrudfv360aZNG+677z7GjBlDeno6L774IsOHD8ff33W10LBhw/jggw945plnGDp0KD/++CP//e9/+f777yte64YbbuCNN94gKSmJtm3bsnbtWv7v//6PoUOHnndbi/vbn1XI+OX7Ttl7NLi9P73yZ2Nf9yQs3Vv5pISOrnDU/g7X5f0i4llMMU3TNHNyckzAzMnJOWldUVGRmZKSYhYVFVlQ2YVLS0sz//SnP5lNmjQxfX19zZCQEPOSSy4x33nnHbOgoMA0TdNs1KiRCZz08/DDD5umaZp79uwxAXPt2rVV9l1QUGDWq1fPfPvttyuWZWdnm88995zZqlUr09/f3wwMDDQ7dOhgvvTSS2ZWVla1dS5YsOCUNQDmnj17Krbbu3evOXDgQDMwMNCMjo42n3rqKbOsrOykfXXq1Mn08/Mzk5OTzXHjxlVZn5ubaz7xxBNmUlKSGRAQYCYnJ5svvPCCWVJSUm197n4cyKk5HE5z4bZMc+i4FWbjZ2eYjUa5fnq8Mc98d/Zm88jqqab59V2m+Wo903wlzPUzuqFpTv+zaR5ca3X5Il7vdN/fNUHzKB3nqfMoSc3RceBZcovL+N/qA/xn2T52HymoWH5VixgebGdwWc4P2NZ/Dfm/6mVN6unqPWpzsy7pF6kjNI+SiEgN2pGRx5fL9jFlzQEKSh2Aa9bs33WJ5cGYFOJ2/BN+WFT5hKBo6HQ3dL4fYlpYVLWIWEVBSUQ8XrnDyfytmXyxdC9Ld1XeVqR5bAiPtS9nQOkc/DZNhLUn7kVouGbJ7nI/tLwOfPysKVxELKegJCIe62hBKd+s3M9Xv+znYLZrDi+bAde3CuPxuE00PfA/jCUrK58Q1gA63wud7oF6jSyqWkTqEgUlEfE4mw7m8PnSvXy3Po3ScteUD/UCfRjRtoDbmU/w9qmwJ9+1sc0HWgyALoOhWR+w2a0rXETqHAWlc6Bx795N//51W5nDycxN6Xy+ZA9r9mdXLL80wWBU/Q10PPwdtk2bK58Qmew6tdbx9xAad/IORURQUDorJ2aGLiwsPGk2a/EehYWumyCf6ZYtcnHlFpcxcUUq45bsIS3HdQ9DXzs8npzBPX6LqLd3Jsax47fqsftDm5tcAanx5ZoUUkTOSEHpLNjtdiIiIsjMzARckzAa+oD1GqZpUlhYSGZmJhEREdjtOjVTFxw4Vsi4JXuZuDKV/JJyAFoGF/BS4nouzf4en9Q9lRvHtXOdWutwBwTWs6hiEXFHCkpn6cR9xE6EJfE+ERERFceBWGddajb/+nk3szal43C65iS9M3I3j4cuoEHmIoy9rkv+8QuB9re7eo/qd1HvkYicFwWls2QYBgkJCcTGxlJWVmZ1OXKR+fr6qifJQg6nybwtGfz7592s3Ou6hN+Hcp5J2MR95nRCs7dA4fGNG17iCkdtbwH/EOuKFhGP4PVBaezYsYwdOxaHw3FW29vtdn1hilwkhaXlTF59gM8W72FvlisJ1bMX8ZcGqxhYMBXfY4dcG/oGuS7p7zYU4tpYWLGIeBrdwuS42p4CXUTOXmZuMV8s28tXy/eTXejqwW0ekM0bCYvplvUdttLjl/YHx0KPh6DbHyAo0sKKRcQquoWJiHiNHRl5/POn3Uxbd5Ayh+v/4fpGHOK5iHkkZ8zBOHS85ze6JVz2J2h/J/jqvnsiUnsUlETEcutSs/lwwU7mpGQcX2Lyx/hdPOL7A1GHf4ET96VtfAVc9jg06ws2m1XliogXUVASEUuYpsnSXVl8uHAnS3a67r/mRxkvJG7kzrJpBGbvcG1o2KHdrdDzT1C/k3UFi4hXUlASkYvK6TSZuyWDDxfuYn1qNgCRtgJeb7Cc/gXf4XP4+BQcfqHQdTD0GAYRidYVLCJeTUFJRC6KMoeT6evT+GjhLnZkugZjN/U5zOj4n+ie/QO2w66b1hJaHy59xBWSAsItrFhEREFJRGpZcZmDSatS+edPuzlwzBWGevnv5qWoH2l5bCHGEddNa4lrD5c95pr/yMfPwopFRCopKIlIrcgrLuOr5fv59897OJJfgg0ntwVt4KmQ2dTPXQ9Hj2/YrK8rIDW5SrNni0ido6AkIjUqp7CMTxfv5vOle8ktLieAEoaH/MJDfjMJL9wPuYDNFzrcCT2HQ1xbq0sWEamWgpKI1IgTAWnckr3klZQTRQ6vhS3kd+Zs/MuyoRzXmKNuf4BLHoKwBKtLFhE5IwUlEbkgOUVlfLp4D+MW7yGvpJxkI423w+bSv3wB9tJS10YRSXDpcOh8r+6/JiJuRUFJRM5LTlEZ45bs4dPFe8grLuMSYyt/DplNz/IVcDwfUb8L9HocWt0Adn3ciIj70SeXiJyT3OIyxi3ey6eLd1NQXMJA2woeC55FS8cO1+k1DGh5nesWI0k9NUBbRNyagpKInJW84jLGLdnLv3/ejaM4jzvtC3k4cDbxZiY4AJ8A6Hi3a4B2dHOryxURqREKSiJyWnnFZXy+ZC//XrwH/6JMhvnM5r6A+YRSACYQFAXdH4Tuf4SQGKvLFRGpUQpKInJKxWUOvli6l48W7cKvMJOnfKZyd8ACfF3n1yCyqev0Wse7wTfQ2mJFRGqJgpKIVFHucDJp9QHem7ed8txMhvtM5/6AefifGKGd1BMuexxaDACbzdpiRURqmYKSiABgmiY/bEzn73O2kXUkgwd9vmdowGyCKHZtkHgpXPMiNLnC2kJFRC4iBSURYfGOI7w9ayt7Dh5iqH0WDwb8QCiFrpX1O7sCUtM+uoJNRLyOgpKIF1ufms2Y2VtZs/Mg99vn8h//6UQY+a6VsW3hmhdcl/orIImIl1JQEvFCuw7n8/c525i/cT9323/kPf9pxBg5rpVRzeHq56DNLRqDJCJeT0FJxIuk5xTz3rztTF29l1uNhSzw/5b6xlHXyohG0Ps5aH+HZtEWETlOn4YiXqCgpJx/LtrFpz/vYIDjZ+b4/I8k22HXyrAGcOVI133Y7L7WFioiUscoKIl4MIfT5H9rDvD3WVvoXvgT3/lMpqnfIdfK4Fi44inoOgR8AyytU0SkrlJQEvFQS3cd4a/TU2iQuYDPfSbR2i8VADOwHkavEXDJg+AXbG2RIiJ1nIKSiIfZfTifN2duJWvLz4z2/Q+d/HYBYPqHYlz2OEaPYRAQZnGVIiLuQUFJxENkF5byj/k7mLNsLU/ZJ3Cr/2IATN8gjEsfwej5JwiKtLhKERH3oqAk4uZKy52M/2UfH8/bxJ1l05jr+x1BRgkmBkbnezCueRlC46wuU0TELSkoibixH7dm8Pr0FFodW8AU369o6HvEtSLxUoyBb7lm1RYRkfOmoCTihvZnFfKX6Zs5tG0Fb/l+SQ+/rQCYYQ0wrn0N2t2m2bRFRGqAgpKIGykuc/Dhwl1MXLSWJ/iGu/wWYDNMTJ8AjF4jMHo9AX5BVpcpIuIxFJRE3IBpmsxNyWD09PX0yfuOuT5TCDOO37S23W0Yff8CEYnWFiki4oEUlETquL1HCnh1+mbYMYdPfcbT1Nc1YaQZ3wFj4NvQ6DKLKxQR8VwKSiJ1VFGpg7ELdjLvp58ZZfuSq/3WA2AGxWD0fRmj0z1gs1tcpYiIZ1NQEqljTNNk9uZ03p2+ijsKvmK6zxx8DQemzdc1H9KVIzVhpIjIRaKgJFKHHMwu4uVv1xO387987fNfonzyADBbDMDoPxqimlpcoYiId1FQEqkDHE6TL5buZdGcKYziC9r47gPAGdUC28A3MZr1tbhCERHvpKAkYrHNaTm8O2ketxz5mC/sKwBw+Idjv+YFbN2Ggt3X4gpFRLyXgpKIRYpKHYyds57A5f9grO17/O1lOLFhdBuK/ernITjK6hJFRLyegpKIBX7afphJ/5vA00Xv08ieCUBp4uX4XT8G4tpaXJ2IiJygoCRyEWXll/DOd6tpk/J/vO8zF2xQHJRAwA3v4Nfqet12RESkjlFQErkITNNk2ro0Zn03gRedH9HQx3Xz2rLOQwjo/7ou9xcRqaMUlERq2eG8Ev76v2X02PkeH/ssAANKQhrif+tYfJN7W12eiIichoKSSC2asSGNmd/+hxecH1Pf5ygAjm5/xP/av4B/iMXViYjImSgoidSCrPwS3pzyCz22/42xPj+BAaVhjfC79UPsjS+3ujwRETlLCkoiNWzWpkPMmvI5zzk+Js4nGxMD5yXD8Ov7EvgFW12eiIicAwUlkRpyrKCUt79dSo9tY3jPvsQ1Fik8Gf/bPsKedKnV5YmIyHlQUBKpAfNSMpg1+d+McvyTGHsOTmw4L30U/z4vgm+g1eWJiMh5UlASuQBFpQ7+b9oSOmx4g7/ZfwEDiiOaEXD7P7E17GZ1eSIicoEUlETO06YD2UwZ/wGPFv2TaHsuTuw4L3ucgKufBd8Aq8sTEZEaoKAkco6cTpOvflxJ7E8v8LJtBRhQEN6C4Dv/ia1BF6vLExGRGqSgJHIOMnKK+N8X73J31ljq2fJxYKe0558J7jMKfPysLk9ERGqYgpLIWZq3bieOqX/iUZaBAUdDW1Hv958QmNDR6tJERKSWKCiJnEFhaTkfT57FDVufobntIOXYybnkz0T1fxbsvlaXJyIitUhBSeQ0dmTk8fXnH/BU4XuE2IrJ840h4PdfEtXkMqtLExGRi0BBSaQa01bv48i0F3jFNh0MyIntQfh9/4HQOKtLExGRi0RBSeQ3issc/H3KYq7Z9Cw32VMAKOz2KOEDXwe7/pMREfEm+tQX+ZW9Rwp4/4uvGJk7mnj7MUptQdhv/YigdjdbXZqIiFhAQUnkuJkb0lj7v3d4iy/wNRwUhDUl+L5vIKaF1aWJiIhFFJTE65WWO/nbjDW0Xv0yz9uXAFDU/EaCb/8Q/EMtrk5ERKykoCReLTO3mL98/h2PHXmNVvZUnNgxr/0LgZf9CQzD6vJERMRiCkritdbsP8bXX3zEm+X/jzBbESUB0fjf9SU07mV1aSIiUkcoKIlXmrRiL1nTX+Zv9mlgQHFCdwLu/g+EJVhdmoiI1CEKSuJVyhxO/u/bJVy2/lnusG8CoLTbwwQMfEOzbIuIyEkUlMRrZOWX8PdxExh+5DUa2LMoswVgv/kD/DrcYXVpIiJSRykoiVfYdCCbmZ+P5pWyT/E3yikIbULwfRMgtrXVpYmISB2moCQeb9a6PRROeZyRtp/AgPwmAwj53b8gIMzq0kREpI5TUBKPZZomX836ic7LHqOtbR9ObJT0fpGQq57Upf8iInJWFJTEI5U5nIz/8hNu3fsXwm2FFPhEEHD3FwQ27W11aSIi4kYUlMTj5BYWM++jp3ggbzwYcDi8PTFDJ0J4A6tLExERN6OgJB7lQPph0v79O24tX+163Oz3NLzrPfDxt7YwERFxSwpK4jE27NqP+Z/buYRtFOPHkd5v07D3UKvLEhERN6agJB5hwbrtRH17Fx2NXeQZwZTcNYmGLXUrEhERuTAKSuL2pi7dQPNZ99LWto88Wxj2wdOIbtTF6rJERMQDKCiJW/tyznJ6LB5KS9sB8uz1CPzjDHwS2lldloiIeAgFJXFLpmny/rSfGLTmYZraDpHnG0PIQ99jxLS0ujQREfEgCkridsodTt6aMJf7tv+JRrZM8vzjCX14JkQmW12aiIh4GJvVBYici+IyBy+Nm86QHY/SyJZJflBDQh+Zq5AkIiK1Qj1K4jbyS8p54V9TeO7wM8QbxygIbULIgz9AWH2rSxMREQ+loCRuIbe4jJc++S8vZj1HjJFDYUQLgv8wA0LjrC5NREQ8mIKS1Hk5hWW88snXvHLseSKNfIqi2hA0dAYER1ldmoiIeDgFJanTjhWU8urH/+G13BcJNwopjOlI0ANTISjS6tJERMQLKChJnXUkv4TRH4/jr3mvEmoUURTXjaAHpkBAuNWliYiIl1BQkjopM6+YMR/9i9cLXifYKKGwfk+CBk8G/xCrSxMRES+ioCR1zuG8Ev724Yf8tXA0AUYZhYlXEXTfN+AXZHVpIiLiZRSUpE45VlDK+x+/z+uFb+JvlFPYuC9B93wFvgFWlyYiIl5IQUnqjNziMj7++F1eyn8bX8NBQfJ1BP/+C/Dxs7o0ERHxUgpKUicUlpbz6YfvMDL3HXwMJ3nNbiL07s/ArkNURESso1uYiOWKyxz856M3eSJnDD6Gk2Mt7iD09+MUkkRExHIeFZRSU1Pp3bs3bdq0oUOHDkyaNMnqkuQMyhxOJn78Gg8f+xs2w+Rwy99T765PwGa3ujQRERHPOvXm4+PDe++9R6dOnUhPT6dr165cd911BAcHW12anILTaTLtny8zOOt9AA61GkLC794Dw7C2MBERkeM8KiglJCSQkJAAQHx8PNHR0Rw9elRBqY76dvz73J7pCkn7Wj9IozvfUUgSEZE6pU6devvpp5+44YYbqF+/PoZhMHXq1JO2GTt2LI0bNyYgIIAePXqwYsWKU+5r9erVOBwOEhMTa7lqOR9TfpjFwF1/BWBn8n0KSSIiUifVqaBUUFBAx44dGTt27CnXT5w4kSeffJJXXnmFNWvW0LFjR/r3709mZmaV7Y4ePcr999/PJ598Uu1rlZSUkJubW+VHLo6ZKzbT7Zc/EWSUkFrvUprd855CkoiI1EmGaZqm1UWcimEYfPvtt9x8880Vy3r06EH37t354IMPAHA6nSQmJvLYY4/x7LPPAq4AdO211/Lggw9y3333Vbv/V199lb/85S8nLc/JySEsLKxm34xUWLo9HXP8bfSybeKoX33qjViCoRvciojIecrNzSU8PLzWvr/rVI/S6ZSWlrJ69Wr69u1bscxms9G3b1+WLVsGgGmaDBkyhGuuuea0IQngueeeIycnp+InNTW1VusXSEnLZftXT9HLtokSI4DwByYpJImISJ3mNkHpyJEjOBwO4uLiqiyPi4sjPT0dgCVLljBx4kSmTp1Kp06d6NSpExs3bjzl/vz9/QkLC6vyI7UnI7eYbz79O0OMGQAYt3yEPaGdxVWJiIicnkdd9Xb55ZfjdDqtLkN+o7jMwVuffcOb5WPBgOJL/0xAh1utLktEROSM3KZHKTo6GrvdTkZGRpXlGRkZxMfHW1SVnIlpmrw6YRFPHXudAKOMwkZ9COj3ktVliYiInBW3CUp+fn507dqV+fPnVyxzOp3Mnz+fnj17WliZnM4Hc7dy044XaGgcoSi0MUF3faZZt0VExG3UqVNv+fn57Ny5s+Lxnj17WLduHZGRkSQlJfHkk08yePBgunXrxiWXXMJ7771HQUEBDzzwgIVVS3W+33CIkJ9eoadPCmX2IALvmwiBEVaXJSIictbqVFBatWoVV199dcXjJ598EoDBgwfz+eef87vf/Y7Dhw/z8ssvk56eTqdOnZg1a9ZJA7zFepsO5rB48nu86TMbAN/b/wWxrSyuSkRE5NzU2XmULrbanofBmxwtKGXke5/xYemL+BtlOK8che2a560uS0REPJDmURK34nCavPzVfP5a+jb+RhllzQZg6/2s1WWJiIicFwUlqVHvz01h8IGXSTCOUhLRzHXKzabDTERE3JO+waTGLNiaSfTPL9Hdtp0ynxD8750IATqNKSIi7uuCBnOnpKSwf/9+SktLqyy/8cYbL6gocT+pRwv5+Zt3eNlnPk4MfO/8DKKbWV2WiIjIBTmvoLR7925uueUWNm7ciGEYnBgPbhy/A7zD4ai5CqXOKy5z8I/PxzPa/BQMcPZ+AVuL/laXJSIicsHO69TbE088QZMmTcjMzCQoKIjNmzfz008/0a1bNxYuXFjDJdausWPH0qZNG7p37251KW7rw+9+5pmcN/AzHBQ1vx6fq562uiQREZEacV7TA0RHR/Pjjz/SoUMHwsPDWbFiBS1btuTHH3/kqaeeYu3atbVRa63S9ADnZ9HmVMIn3kQn2y7yw1sQ8ugC8A+xuiwREfESdXJ6AIfDQWhoKOAKTWlpaQA0atSIbdu21Vx1Uqcdzi0me/LjdLLtosgeSsjgiQpJIiLiUc5rjFK7du1Yv349TZo0oUePHowZMwY/Pz8++eQTkpOTa7pGqYOcTpP/fvE+w80fcWDDfuc4iNS/vYiIeJbzCkovvvgiBQUFALz22mtcf/31XHHFFURFRTFx4sQaLVDqpvE/beL2Ix+AAdldHyOq5bVWlyQiIlLjziso9e9feUVTs2bN2Lp1K0ePHqVevXoVV76J50pJy8UxfzRx9mxygxKJGqDbk4iIiGc6pzFKTqeTt99+m169etG9e3eeffZZioqKAIiMjFRI8gJlDidjJ3zLfbZZAITe8h74BlhblIiISC05p6D0xhtv8PzzzxMSEkKDBg34xz/+wfDhw2urNqmDPvxxB0Nz3sfHcFLc4kaM5n2tLklERKTWnFNQ+vLLL/nwww+ZPXs2U6dOZfr06Xz11Vc4nc7aqk/qkJS0XNIX/Zuuth2U+wQRcP3bVpckIiJSq84pKO3fv5/rrruu4nHfvn0xDKNiegDxXGUOJ6//9yeesX8NgP2a5yGsvsVViYiI1K5zCkrl5eUEBFQdj+Lr60tZWVmNFiV1z0cLd3HTkX9Rz8inLKYNRo9HrC5JRESk1p3TVW+maTJkyBD8/f0rlhUXFzNs2DCCg4Mrlk2ZMqXmKhTL7cjIY8mCGUz0WQiA7w3vgv2C7qcsIiLiFs7p227w4MEnLbv33ntrrBipe0zT5KUp63nV9qnrcad7MZIutbgqERGRi+OcgtK4ceNqqw6poyavPkDbAxNo7ZuKI6Ae9mtfs7okERGRi0bnT6RaxwpK+fSHJUz2mQyA/dq/QHCUxVWJiIhcPOcUlIYOHXpW23322WfnVYzULWNmb+VPZZ8RYi/G2bA7ts73WV2SiIjIRXVOQenzzz+nUaNGdO7cGdM0a6smqQNW7zvGwVUzuN5vOaZhw3b9u2A7p4skRURE3N45BaVHHnmECRMmsGfPHh544AHuvfdeIiMja6u2i2Ls2LGMHTsWh8NhdSl1htNp8tdpa/g/n88BMHoMg/j21hYlIiJiAcM8x66hkpISpkyZwmeffcbSpUsZNGgQf/jDH+jXr59b3+stNzeX8PBwcnJyCAsLs7ocS01alcqBb1/hz77/wxEch/2xVRDg3W0iIiJ1U21/f5/zuRR/f3/uvvtu5s6dS0pKCm3btuXRRx+lcePG5Ofn13iBcnEVlpYzYdZCHvX5DgD7wDcVkkRExGtd0KATm82GYRiYpqlTVx7i44W7eKLkE/yNMpxNekPbW60uSURExDLnHJRKSkqYMGEC1157LS1atGDjxo188MEH7N+/n5CQkNqoUS6SQzlF7Pv5a66yb8Bh88U26O/gxqdTRURELtQ5DeZ+9NFH+eabb0hMTGTo0KFMmDCB6Ojo2qpNLrL/9/1anrV9CYDt8hEQ3czagkRERCx2TkHp448/JikpieTkZBYtWsSiRYtOuZ3u9eZ+tqXnEZPyKQk+RykJTcL/iqesLklERMRy5xSU7r//fre+sk2q9/6sdbxmnwWAf79XwDfQ4opERESsd84TTornWZ+aTdSOSUT65lMWloRvm5utLklERKRO0FTLwruzN/Ogz/cA+F7+ONh1C0ARERFQUPJ6y3dnEb57Bg2NIzgCo6DzvVaXJCIiUmcoKHm5d+duY5jPDADslz6isUkiIiK/oqDkxVbvO0rAvgW0tu3H6RsMl/zR6pJERETqlHMKSi+//DKrV6+urVrkIvtwwS6G+UwHwNbtAQisZ3FFIiIidcs5BaUDBw4wcOBAGjZsyCOPPMLMmTMpLS2trdqkFm05lEvWtqVcatuCafOFSx+1uiQREZE655yC0meffUZ6ejoTJkwgNDSUESNGEB0dzW233caXX37J0aNHa6tOqWEfLazsTTI63AnhDSyuSEREpO455zFKNpuNK664gjFjxrBt2zaWL19Ojx49+Oc//0n9+vW58sor+dvf/sbBgwdro16pAfuyCti8cRX9bKtcC3o9YW1BIiIiddQFD+Zu3bo1zzzzDEuWLCE1NZXBgwfz888/M2HChJqoT2rBuCV7edA2A5thQsvrIKal1SWJiIjUSYZpmqbVRVhp7NixjB07FofDwfbt28nJySEsLMzqsmpNbnEZN46exGzjMfyNchg6B5J6WF2WiIjIecnNzSU8PLzWvr+9fnqA4cOHk5KSwsqVK60u5aKYvOoAdzm/x98ox0zqqZAkIiJyGrpXhRdxOE0mL93MRPt8AIxeI6wtSEREpI7z+h4lb7JgaybtcxYSahThjGoOzftZXZKIiEiddkFB6eDBg7q6zY18sWwvt9gXA2DrfA/YlJNFRERO57y+KZcsWUKTJk1ISkoiKSmJuLg4Ro0aRW5ubk3XJzUk9Wghu3dscU0wiQHt77C6JBERkTrvvILSww8/TOvWrVm5ciXbtm3jnXfeYd68eXTp0kU9THXUpFWp3GRfCoDR+HIIb2hxRSIiInXfeU0PEBgYyPr162nRokXFMtM0ufPOOwGYNGlSzVV4kdT25YVWcjhNer05n/+UPE5z20G4aSx0vtfqskRERC5YnZweoHXr1mRmZlZZZhgGr732GrNmzaqRwqTm/LT9MFH5W2luO4jpEwCtb7S6JBEREbdwXkFpyJAhPPbYY6SmplZZ7om9MZ7gm5X7ufX4IG6j5XUQoH8jERGRs3Fe8yiNGDECgObNm3PrrbfSqVMnHA4H48ePZ8yYMTVZn1ygYwWlLNxyiL/6usYn0eF31hYkIiLiRs4rKB06dIh169axfv161q1bx+eff86OHTswDIMxY8Ywc+ZMOnToQIcOHRgwYEBN1yznYOamdC5lIzFGDgRFQbM+VpckIiLiNs4rKMXFxdG/f3/69+9fsay4uJiNGzdWBKjvvvuO0aNHk52dXVO1ynmYtu4gdx0/7Ua728Dua21BIiIibqTGbmESEBBA9+7d6d69e03tUi5QWnYRm/am0d9vlWtBh7usLUhERMTNaGpmDzZjQxr9jJUEGSUQ2RQadLG6JBEREbeioOTBpq8/VHHLEjreBYZhbUEiIiJuRkHJQx3MLmLPwUP0tKW4FrS7zdqCRERE3JCCkoeauzmdnrYUfA2H67RbVFOrSxIREXE7Ckoeak5KBlfZ1rseaEoAERGR86Kg5IGOFZSyfE8WV9k2uBY0VVASERE5HwpKHujHrZkkmYdItB0Gmy80vtzqkkRERNyS1welsWPH0qZNG4+a/2nh9sNceaI3qVFP8A+xtiARERE35fVBafjw4aSkpLBy5UqrS6kRDqfJ4h2/Cko67SYiInLevD4oeZpNB3MoKCysnBZAA7lFRETOm4KSh/l5x2G62ba5ZuMOiYO4dlaXJCIi4rYUlDzMT9uPVE4L0LSPZuMWERG5AApKHqSo1MGa/ce40rbRtUCn3URERC6IgpIHWbv/GAHOAlraUl0LGl9hbUEiIiJuTkHJgyzfc5T2tj3YMCE8EULjrC5JRETErSkoeZAVe47SwdjtelC/s7XFiIiIeAAFJQ9RWu5kzf5jdLDtci1o0NXagkRERDyAgpKH2JyWQ0m5k872Pa4FDbpYW5CIiIgHUFDyEBsO5BBFDvU5DBiQ0MnqkkRERNyegpKHWH8gmw624+OToltAQJi1BYmIiHgABSUPseFADh0rxifptJuIiEhNUFDyAHnFZew6nE9HQwO5RUREapKCkgdIScvFNE06nRjIXV89SiIiIjVBQckDbMvII4Gj1CMXbL4QrxvhioiI1AQFJQ+wNT2PZFua60FkE/Dxt7YgERERD6Gg5AG2p+fR2MhwPYhsam0xIiIiHkRByc2Zpsm2jDwaG+muBZHJ1hYkIiLiQRSU3FxGbgl5xeU0th3vUYpSUBIREakpCkpubm9WAQDN7SdOvSkoiYiI1BQFJTe3L6sAG04amBqjJCIiUtMUlNzc3qxCEsjClzKw+0F4Q6tLEhER8RgKSm5uX1YBjW3HB3LXaww2u6X1iIiIeBKvD0pjx46lTZs2dO/e3epSzkvq0aJfTQ2g8UkiIiI1yeuD0vDhw0lJSWHlypVWl3JeDuUU00hzKImIiNQKrw9K7qy03MmR/BISjCzXAo1PEhERqVEKSm4sI7cYgGgjz7UgJNbCakRERDyPgpIbSz8elOLsx4NScLSF1YiIiHgeBSU3diSvBIAoclwLgmMsrEZERMTzKCi5saOFpdhwEmrmuhYoKImIiNQoBSU3dqyglHrkYcMEDAiMtLokERERj6Kg5MaOFpQRbRw/7RYUCXYfawsSERHxMApKbiy7qJQoQ6fdREREaouCkhsrKnUQSqHrQUC4tcWIiIh4IAUlN1ZU5sCfMtcDnwBrixEREfFACkpurLjMQYBR6nqgoCQiIlLjFJTcWFGZs7JHyVdBSUREpKYpKLmx4lIHAahHSUREpLYoKLkxjVESERGpXQpKbqzM4cTfUFASERGpLQpKbsxmGL869eZvbTEiIiIeSEHJjdls/Gowd6C1xYiIiHggBSU3ZjOMyqBk97O2GBEREQ+koOTG7IaB48Q/oem0thgREREPpKDkxgwDSjl+I1xHqbXFiIiIeCAFJTdmtxmUKSiJiIjUGgUlNxbk5/OroFRmbTEiIiIeSEHJjYUG+KhHSUREpBYpKLmxsABfSk0FJRERkdqioOTGQgN8fjWYW6feREREapqCkhvTqTcREZHapaDkxkIDfCnF1/WgvMTaYkRERDyQgpIbiwz2I8cMdj0oyra0FhEREU/k9UFp7NixtGnThu7du1tdyjmLDwvgGCGuB4VZ1hYjIiLigbw+KA0fPpyUlBRWrlxpdSnnLD48gGzzeFAqOmptMSIiIh7I64OSO4sPD+CoGQqAWZgFpmlxRSIiIp5FQcmNRQb5UWAPB8BwlkNJnsUViYiIeBYFJTdmsxmEh4VSaPq7FmickoiISI1SUHJzifWCKgd0a5ySiIhIjVJQcnNNY4MrximRf9jaYkRERDyMgpKbaxYTQpoZ7XqQk2ptMSIiIh5GQcnNNY0N4eCJoJS939piREREPIyCkptrGhPCATMGAOcxBSUREZGapKDk5hLCAzhsjwWgNGuvtcWIiIh4GAUlN2cYBv7RjV0PNEZJRESkRikoeYCYxOYABJRkQWmhxdWIiIh4DgUlD9CyUSLZZrDrQdZOa4sRERHxIApKHqBDYgRbzSQAyg9ttLgaERERz6Gg5AEaRwWzy9YIgOw9ay2uRkRExHMoKHkAm82gqF5rAEoPqkdJRESkpigoeYiwxp0ACMneCqZpbTEiIiIeQkHJQzRvfwkO0yDMmY0zL8PqckRERDyCgpKHaN8onn0kALA/ZYXF1YiIiHgGBSUP4WO3kRXcDICMHastrkZERMQzKCh5ECO+PQCOdA3oFhERqQkKSh4kvkU3AKLyd1BYWm5xNSIiIu5PQcmDNGjlCkrJHGTp1gMWVyMiIuL+FJQ8iBGeSJ5vNL6Gg51rFlpdjoiIiNtTUPIkhkFx/Utdf+5bjMOp+ZREREQuhIKSh4lsezUAHco3sy4129piRERE3JyCkoexN7kSgM62HczbuN/iakRERNybgpKniW5OiX80AUYZe9f/hFOn30RERM6bgpKnMQx8knsB0LRwPav3H7O4IBEREfeloOSB7E2uAKCHbQvfrUuzuBoRERH3paDkiRq5epS62nYwZ8N+yh1OiwsSERFxTwpKniimFWZwLEFGCU2LN7J45xGrKxIREXFLCkqeyGbDaNEPgL62NUxarVm6RUREzoeCkqdqMRCAPrY1zN2czrGCUosLEhERcT8KSp4quTfY/WhkyyTReYBv1x60uiIRERG3o6DkqfxD4Pjkk9fY1jJxZSqmqTmVREREzoWCkidrMQCAa33Wsi0jj/UHciwuSERExL0oKHmyFv0B6Gpspx65jP9ln8UFiYiIuBevD0pjx46lTZs2dO/e3epSal5EEiR0wo6DQfblfLcujSP5JVZXJSIi4ja8PigNHz6clJQUVq5caXUptaPD7wC4N/AXSh1Ovl6uG+WKiIicLa8PSh6v3W1g2GhVvoUkI4P//LKP0nLN1C0iInI2FJQ8XWgcJF8NwL1Bv3A4r4TvN+r+byIiImdDQckbHD/9dqffUsDks8V7NVWAiIjIWVBQ8gatrwffYCKKUunus5uNB3NYtivL6qpERETqPAUlb+AX7ApLwNPx6wB4b94O9SqJiIicgYKSt+hwJwDdCxYS5ONkxd6j6lUSERE5AwUlb9GkNwTHYivK4sWWhwB4d9529SqJiIichoKSt7D7QPvbAbjVZzF+PjZW7j3GUvUqiYiIVEtByZscv/otYNdsHugaBcC7c9WrJCIiUh0FJW+S0BGiW0J5McPjU/D3sbFq3zGW7FSvkoiIyKkoKHkTw6gY1B22/X/8vkcSoLFKIiIi1VFQ8jbt73D93vMzw7sE4u9jY/W+Y/y844i1dYmIiNRBCkrepl4jSLoMMIneO517ejQC4D31KomIiJxEQckbdXQN6mbDfxnWO5kAXxtr9mfzk3qVREREqlBQ8kZtbgK7H2RsIrZgJ/eqV0lEROSUFJS8UWA9aNHf9feGiTx8VVMCfG2s3Z/Nou2Hra1NRESkDlFQ8lbH51Ri42Rign2471JXr9I/5usecCIiIicoKHmr5v0gIALy0mDvYh66sil+Pq5epZV7j1ldnYiISJ2goOStfPyh7S2uvzdMJCbUn9u7NgTgk592WViYiIhI3aGg5M2OTz7JlulQXsKDVyRjGDBvSyb7sgqsrU1ERKQOUFDyZomXQlgDKMmFHXNpEh3M5c2iAZi06oDFxYmIiFhPQcmb2WyVp982TQbgd90TAZi8+gAOpwZ1i4iId1NQ8nbtb3f93jYLSvK5tk0coQE+pOcWsy5Vg7pFRMS7KSh5u4ROEJkM5UWwbSb+PnauaRULwOzNGdbWJiIiYjEFJW9nGNDuNtffW6cD0Kd1HIBulCsiIl5PQUmg5UDX750/QnkpPZOjANiankt+SbmFhYmIiFhLQUkgoTOExEFpHuxbQkyoPwnhAZgmbD2Ua3V1IiIillFQEtfVb837uf7ePguANglhAKQoKImIiBdTUBKXFgNcv7fNBNOkeVwoADsz8y0sSkRExFoKSuKS3BtsvpC9D7L3ERvqD0BWQam1dYmIiFhIQUlc/EOgfmfX3/uWEhXiB0BWfomFRYmIiFhLQUkqNbrM9XvfUqJDjvco5atHSUREvJeCklSqCEpLCPKzA1BY6rCwIBEREWspKEmlxEtcv4/uxizKAcDXblhYkIiIiLUUlKRSYD0Id90U15G+CYDwQF8rKxIREbGUgpJUFdcOgLID6wFICA+0shoRERFLKShJVfGuoGRmbgagfcNwK6sRERGxlIKSVBXZFACf3FQAOiVGWFiMiIiItRSUpKqIJABiHRmEB/rSvXGkxQWJiIhYR0FJqjoelBoYR7ilYzx+PjpERETEe+lbUKrYURRCuWnDz3DwUNdgq8sRERGxlI/VBUjd0jyhHvuueJNd+f5cExdvdTkiIiKWUlCSkzTqO4xGVhchIiJSB+jUm4iIiEg1FJREREREqqGgJCIiIlINBSURERGRaigoiYiIiFRDQUlERESkGgpKIiIiItVQUBIRERGphoKSiIiISDUUlERERESqoVuYHGeaJgC5ubkWVyIiIiJn68T39onv8Zrm9UFp7NixjB07lpKSEgASExMtrkhERETOVVZWFuHh4TW+X8OsrQjmZrKzs6lXrx779++vlYZ2Z7m5uSQmJpKamkpYWJjV5dQpapvqqW2qp7apntrm1NQu1cvJySEpKYljx44RERFR4/v3+h6lE2w213Ct8PBwHYTVCAsLU9tUQ21TPbVN9dQ21VPbnJrapXonvsdrfL+1slcRERERD6CgJCIiIlINBaXj/P39eeWVV/D397e6lDpHbVM9tU311DbVU9tUT21zamqX6tV222gwt4iIiEg11KMkIiIiUg0FJREREZFqKCiJiIiIVENBSURERKQaHh+UDh48yL333ktUVBSBgYG0b9+eVatWVaw3TZOXX36ZhIQEAgMD6du3Lzt27Kiyj6NHj3LPPfcQFhZGREQEf/jDH8jPz7/Yb6XGnalthgwZgmEYVX4GDBhQZR+e2DaNGzc+6X0bhsHw4cMBKC4uZvjw4URFRRESEsJtt91GRkZGlX3s37+fQYMGERQURGxsLCNHjqS8vNyKt1OjztQ2vXv3PmndsGHDquzDU9vG4XDw0ksv0aRJEwIDA2natCmvv/56lftPeePnzdm0i7d+1gDk5eUxYsQIGjVqRGBgIJdddhkrV66sWO+Nx8wJZ2qbi3bcmB7s6NGjZqNGjcwhQ4aYy5cvN3fv3m3Onj3b3LlzZ8U2b731lhkeHm5OnTrVXL9+vXnjjTeaTZo0MYuKiiq2GTBggNmxY0fzl19+MX/++WezWbNm5t13323FW6oxZ9M2gwcPNgcMGGAeOnSo4ufo0aNV9uOJbZOZmVnlPc+dO9cEzAULFpimaZrDhg0zExMTzfnz55urVq0yL730UvOyyy6reH55ebnZrl07s2/fvubatWvNH374wYyOjjafe+45i95RzTlT21x11VXmgw8+WGWbnJyciud7ctu88cYbZlRUlDljxgxzz5495qRJk8yQkBDzH//4R8U23vh5czbt4q2fNaZpmnfeeafZpk0bc9GiReaOHTvMV155xQwLCzMPHDhgmqZ3HjMnnKltLtZx49FBadSoUebll19e7Xqn02nGx8eb77zzTsWy7Oxs09/f35wwYYJpmqaZkpJiAubKlSsrtpk5c6ZpGIZ58ODB2iu+lp2pbUzTdRDedNNN1a731Lb5rSeeeMJs2rSp6XQ6zezsbNPX19ecNGlSxfotW7aYgLls2TLTNE3zhx9+MG02m5menl6xzUcffWSGhYWZJSUlF73+2vTrtjFNV1B64oknqt3ek9tm0KBB5tChQ6ssu/XWW8177rnHNE3v/bw5U7uYpvd+1hQWFpp2u92cMWNGleVdunQxX3jhBa89ZkzzzG1jmhfvuPHoU2/fffcd3bp144477iA2NpbOnTvzr3/9q2L9nj17SE9Pp2/fvhXLwsPD6dGjB8uWLQNg2bJlRERE0K1bt4pt+vbti81mY/ny5RfvzdSwM7XNCQsXLiQ2NpaWLVvyyCOPkJWVVbHOU9vm10pLSxk/fjxDhw7FMAxWr15NWVlZlWOmVatWJCUlVTlm2rdvT1xcXMU2/fv3Jzc3l82bN1/091Bbfts2J3z11VdER0fTrl07nnvuOQoLCyvWeXLbXHbZZcyfP5/t27cDsH79ehYvXszAgQMB7/28OVO7nOCNnzXl5eU4HA4CAgKqLA8MDGTx4sVee8zAmdvmhItx3Hj0TXF3797NRx99xJNPPsnzzz/PypUrefzxx/Hz82Pw4MGkp6cDVPnQPvH4xLr09HRiY2OrrPfx8SEyMrJiG3d0prYBGDBgALfeeitNmjRh165dPP/88wwcOJBly5Zht9s9tm1+berUqWRnZzNkyBDAdTz4+fmddIfq3x4zpzqmTqzzFL9tG4Df//73NGrUiPr167NhwwZGjRrFtm3bmDJlCuDZbfPss8+Sm5tLq1atsNvtOBwO3njjDe655x4Ar/28OVO7gPd+1oSGhtKzZ09ef/11WrduTVxcHBMmTGDZsmU0a9bMa48ZOHPbwMU7bjw6KDmdTrp168bo0aMB6Ny5M5s2beLjjz+uCAPe6mza5q677qrYvn379nTo0IGmTZuycOFC+vTpY0ndF9unn37KwIEDqV+/vtWl1DmnapuHHnqo4u/27duTkJBAnz592LVrF02bNrWizIvmv//9L1999RVff/01bdu2Zd26dYwYMYL69et79efN2bSLN3/W/Oc//2Ho0KE0aNAAu91Oly5duPvuu1m9erXVpVnuTG1zsY4bjz71lpCQQJs2baosa926Nfv37wcgPj4e4KQrljIyMirWxcfHk5mZWWV9eXk5R48erdjGHZ2pbU4lOTmZ6Ohodu7cCXhu25ywb98+5s2bxx//+MeKZfHx8ZSWlpKdnV1l298eM6c6pk6s8wSnaptT6dGjB0CVY8ZT22bkyJE8++yz3HXXXbRv35777ruPP//5z7z55puA937enKldTsWbPmuaNm3KokWLyM/PJzU1lRUrVlBWVkZycrLXHjMnnK5tTqW2jhuPDkq9evVi27ZtVZZt376dRo0aAdCkSRPi4+OZP39+xfrc3FyWL19Oz549AejZsyfZ2dlV0v2PP/6I0+ms+BJwR2dqm1M5cOAAWVlZJCQkAJ7bNieMGzeO2NhYBg0aVLGsa9eu+Pr6Vjlmtm3bxv79+6scMxs3bqzyH+jcuXMJCws7KZy6q1O1zamsW7cOoMox46ltU1hYiM1W9SPVbrfjdDoB7/28OVO7nIq3fdYABAcHk5CQwLFjx5g9ezY33XST1x4zv3WqtjmVWjtuzm0cuntZsWKF6ePjY77xxhvmjh07zK+++soMCgoyx48fX7HNW2+9ZUZERJjTpk0zN2zYYN50002nvPSyc+fO5vLly83FixebzZs3d/tLL8/UNnl5eebTTz9tLlu2zNyzZ485b948s0uXLmbz5s3N4uLiiv14YtuYpmk6HA4zKSnJHDVq1Enrhg0bZiYlJZk//vijuWrVKrNnz55mz549K9afuAS+X79+5rp168xZs2aZMTExHnEJvGlW3zY7d+40X3vtNXPVqlXmnj17zGnTppnJycnmlVdeWbGNJ7fN4MGDzQYNGlRcBj9lyhQzOjrafOaZZyq28cbPmzO1i7d/1syaNcucOXOmuXv3bnPOnDlmx44dzR49epilpaWmaXrnMXPC6drmYh43Hh2UTNM0p0+fbrZr18709/c3W7VqZX7yySdV1judTvOll14y4+LiTH9/f7NPnz7mtm3bqmyTlZVl3n333WZISIgZFhZmPvDAA2ZeXt7FfBu14nRtU1hYaPbr18+MiYkxfX19zUaNGpkPPvhglcu6TdNz22b27NkmcNKxYJqmWVRUZD766KNmvXr1zKCgIPOWW24xDx06VGWbvXv3mgMHDjQDAwPN6Oho86mnnjLLysouVvm1qrq22b9/v3nllVeakZGRpr+/v9msWTNz5MiRVeZRMk3PbZvc3FzziSeeMJOSksyAgAAzOTnZfOGFF6pMe+CNnzdnahdv/6yZOHGimZycbPr5+Znx8fHm8OHDzezs7Ir13njMnHC6trmYx41hmr+aHlVEREREKnj0GCURERGRC6GgJCIiIlINBSURERGRaigoiYiIiFRDQUlERESkGgpKIiIiItVQUBIRERGphoKSiIiISDUUlERERESqoaAkIiIiUg0FJRFxG7Nnz8YwjNP+zJkz55TPfeCBB3jxxRdPuW7IkCHcfPPNVZZNnjyZgIAA/v73v9f02xARN+JjdQEiImfryiuv5NChQxWP27Vrx6OPPsqjjz5asSwmJuak5zkcDmbMmMH3339/Vq/z73//m+HDh/Pxxx/zwAMPXHjhIuK2FJRExG0EBgYSGBgIwMGDB8nKyuKKK64gPj7+tM9bunQpvr6+dO/e/YyvMWbMGF555RW++eYbbrnllhqpW0Tcl4KSiLiltWvXAtClS5czbvvdd99xww03YBjGabcbNWoUH374ITNmzKBPnz41UqeIuDcFJRFxS2vWrCExMZGoqKgzbjtt2jTefffd024zc+ZMpk2bxvz587nmmmtqqkwRcXMazC0ibmnNmjVn1Zu0ZcsW0tLSzthD1KFDBxo3bswrr7xCfn5+TZUpIm5OQUlE3NLZBqXvvvuOa6+9loCAgNNu16BBAxYuXMjBgwcZMGAAeXl5NVWqiLgxBSURcTtHjhwhNTX1rILStGnTuOmmm85qv40aNWLRokWkp6crLIkIoKAkIm5ozZo1wJkHcmdmZrJq1Squv/76s953YmIiCxcuJDMzk/79+5Obm3tBtYqIe1NQEhG3s3btWuLi4qhfv/5pt5s+fTqXXHIJ0dHR57T/hg0bsnDhQo4cOaKwJOLlDNM0TauLEBGpDTfeeCOXX345zzzzjNWliIibUo+SiHisyy+/nLvvvtvqMkTEjalHSURERKQa6lESERERqYaCkoiIiEg1FJREREREqqGgJCIiIlINBSURERGRaigoiYiIiFRDQUlERESkGgpKIiIiItVQUBIRERGpxv8HDilogOAqeCoAAAAASUVORK5CYII=", "text/plain": [ "
" ] }, "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');" ] }, { "cell_type": "markdown", "id": "933a88ef", "metadata": {}, "source": [ "## Critical points\n", "\n", "If you have a relatively simple critical curve for a binary mixture and you would like to obtain the critical point at a given composition, you can obtain it reliably in a multi-step process:\n", "\n", "1. Trace the binary curve \n", "2. Interpolate to find the approximate value for critical temperature and density\n", "3. Use Newton's method to solve the criticality conditions from estimated critical point\n", "4. Calculate whatever else you want" ] }, { "cell_type": "code", "execution_count": 6, "id": "4618df2a", "metadata": { "execution": { "iopub.execute_input": "2025-10-15T23:08:13.673229Z", "iopub.status.busy": "2025-10-15T23:08:13.673099Z", "iopub.status.idle": "2025-10-15T23:08:13.887950Z", "shell.execute_reply": "2025-10-15T23:08:13.887366Z" } }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "df = get_critical_curve([name0, othername], ipure)\n", "model = teqp.build_multifluid_model([name0, othername], teqp.get_datapath())\n", "line, = plt.plot(df['T / K'], df['p / Pa']/1e6, '-')\n", "rhotot = df['rho0 / mol/m^3']+df['rho1 / mol/m^3']\n", "\n", "# Build cubic interpolators between the variables\n", "tinterp = scipy.interpolate.interp1d(df['z0 / mole frac.'], df['t'], kind='cubic') # interpolator from mole fraction to tracing parameter\n", "Tinterp = scipy.interpolate.interp1d(df['t'], df['T / K'], kind='cubic')\n", "rhointerp = scipy.interpolate.interp1d(df['t'], rhotot, kind='cubic')\n", "\n", "# Iterate over composition\n", "for x0 in np.arange(0.1, 1, 0.05):\n", "\n", " molefracs = np.array([x0, 1-x0])\n", " \n", " # Initial guess for critical point from interpolation\n", " t = tinterp(x0)\n", " T0 = Tinterp(t)\n", " rho0 = rhointerp(t)\n", " p0 = rho0*model.get_R(molefracs)*T0*(1+model.get_Ar01(T0, rho0, molefracs))\n", " plt.plot(T0, p0/1e6, 'o')\n", " \n", " # Newton iteration for the correct critical point\n", " def resid(x):\n", " return model.get_criticality_conditions(T=x[0], rhovec=x[1]*molefracs)\n", " soln = scipy.optimize.fsolve(resid, x0=[T0, rho0])\n", " T, rho = soln\n", " p = rho*model.get_R(molefracs)*T*(1+model.get_Ar01(T, rho, molefracs))\n", " plt.plot(T, p/1e6, '+')\n", "# print(x0, T0, rho0, p0, resid([T0, rho0]), T, rho, resid([T, rho]))\n", "\n", "elap = timeit.default_timer()-tic\n", "plt.gca().set(xlabel='$T$ / K', ylabel='$p$ / MPa')\n", "plt.tight_layout(pad=0.2)" ] } ], "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": "3.11.14" } }, "nbformat": 4, "nbformat_minor": 5 }