1{ 2 "cells": [ 3 { 4 "cell_type": "markdown", 5 "metadata": {}, 6 "source": [ 7 "# Pincell Depletion\n", 8 "This notebook is intended to introduce the reader to the depletion interface contained in OpenMC. It is recommended that you are moderately familiar with building models using the OpenMC Python API. The earlier examples are excellent starting points, as this notebook will not focus heavily on model building.\n", 9 "\n", 10 "If you have a real power reactor, the fuel composition is constantly changing as fission events produce energy, remove some fissile isotopes, and produce fission products. Other reactions, like $(n, \\alpha)$ and $(n, \\gamma)$ will alter the composition as well. Furthermore, some nuclides undergo spontaneous decay with widely ranging frequencies. Depletion is the process of modeling this behavior.\n", 11 "\n", 12 "In this notebook, we will model a simple fuel pin in an infinite lattice using the Python API. We will then build and examine some of the necessary components for performing depletion analysis. Then, we will use the depletion interface in OpenMC to simulate the fuel pin producing power over several months. Lastly, we will wrap up with some helpful tips to improve the fidelity of depletion simulations." 13 ] 14 }, 15 { 16 "cell_type": "code", 17 "execution_count": 1, 18 "metadata": {}, 19 "outputs": [], 20 "source": [ 21 "%matplotlib inline\n", 22 "import math\n", 23 "import openmc" 24 ] 25 }, 26 { 27 "cell_type": "markdown", 28 "metadata": {}, 29 "source": [ 30 "## Build the Geometry\n", 31 "\n", 32 "Much of this section is borrowed from the \"Modeling a Pin-Cell\" example. If you find yourself not understanding some aspects of this section, feel free to refer to that example, as some details may be glossed over for brevity.\n", 33 "\n", 34 "First, we will create our fuel, cladding, and water materials to represent a typical PWR." 35 ] 36 }, 37 { 38 "cell_type": "code", 39 "execution_count": 2, 40 "metadata": {}, 41 "outputs": [], 42 "source": [ 43 "fuel = openmc.Material(name=\"uo2\")" 44 ] 45 }, 46 { 47 "cell_type": "code", 48 "execution_count": 3, 49 "metadata": {}, 50 "outputs": [], 51 "source": [ 52 "fuel.add_element(\"U\", 1, percent_type=\"ao\", enrichment=4.25)\n", 53 "fuel.add_element(\"O\", 2)\n", 54 "fuel.set_density(\"g/cc\", 10.4)" 55 ] 56 }, 57 { 58 "cell_type": "code", 59 "execution_count": 4, 60 "metadata": {}, 61 "outputs": [], 62 "source": [ 63 "clad = openmc.Material(name=\"clad\")" 64 ] 65 }, 66 { 67 "cell_type": "code", 68 "execution_count": 5, 69 "metadata": {}, 70 "outputs": [], 71 "source": [ 72 "clad.add_element(\"Zr\", 1)\n", 73 "clad.set_density(\"g/cc\", 6)" 74 ] 75 }, 76 { 77 "cell_type": "code", 78 "execution_count": 6, 79 "metadata": {}, 80 "outputs": [], 81 "source": [ 82 "water = openmc.Material(name=\"water\")" 83 ] 84 }, 85 { 86 "cell_type": "code", 87 "execution_count": 7, 88 "metadata": {}, 89 "outputs": [], 90 "source": [ 91 "water.add_element(\"O\", 1)\n", 92 "water.add_element(\"H\", 2)\n", 93 "water.set_density(\"g/cc\", 1.0)" 94 ] 95 }, 96 { 97 "cell_type": "code", 98 "execution_count": 8, 99 "metadata": {}, 100 "outputs": [], 101 "source": [ 102 "water.add_s_alpha_beta(\"c_H_in_H2O\")" 103 ] 104 }, 105 { 106 "cell_type": "code", 107 "execution_count": 9, 108 "metadata": {}, 109 "outputs": [], 110 "source": [ 111 "materials = openmc.Materials([fuel, clad, water])" 112 ] 113 }, 114 { 115 "cell_type": "markdown", 116 "metadata": {}, 117 "source": [ 118 "Here, we are going to use the `openmc.model.pin` function to build our pin cell. The `pin` function anticipates concentric cylinders and materials to fill the inner regions. One additional material is needed than the number of cylinders to cover the domain outside the final ring. \n", 119 "\n", 120 "To do this, we define two radii for the outer radius of our fuel pin, and the outer radius of the cladding." 121 ] 122 }, 123 { 124 "cell_type": "code", 125 "execution_count": 10, 126 "metadata": {}, 127 "outputs": [], 128 "source": [ 129 "radii = [0.42, 0.45]" 130 ] 131 }, 132 { 133 "cell_type": "markdown", 134 "metadata": {}, 135 "source": [ 136 "Using these radii, we define concentric `ZCylinder` objects. So long as the cylinders are concentric and increasing in radius, any orientation can be used. We also take advantage of the fact that the `openmc.Materials` object is a subclass of the `list` object to assign materials to the regions defined by the surfaces." 137 ] 138 }, 139 { 140 "cell_type": "code", 141 "execution_count": 11, 142 "metadata": {}, 143 "outputs": [], 144 "source": [ 145 "pin_surfaces = [openmc.ZCylinder(r=r) for r in radii]" 146 ] 147 }, 148 { 149 "cell_type": "code", 150 "execution_count": 12, 151 "metadata": {}, 152 "outputs": [], 153 "source": [ 154 "pin_univ = openmc.model.pin(pin_surfaces, materials)" 155 ] 156 }, 157 { 158 "cell_type": "markdown", 159 "metadata": {}, 160 "source": [ 161 "The first material, in our case `fuel`, is placed inside the first cylinder in the inner-most region. The second material, `clad`, fills the space between our cylinders, while `water` is placed outside the last ring. The `pin` function returns an `openmc.Universe` object, and has some additional features we will mention later." 162 ] 163 }, 164 { 165 "cell_type": "code", 166 "execution_count": 13, 167 "metadata": {}, 168 "outputs": [ 169 { 170 "data": { 171 "text/plain": [ 172 "<matplotlib.image.AxesImage at 0x7f9aea1a50d0>" 173 ] 174 }, 175 "execution_count": 13, 176 "metadata": {}, 177 "output_type": "execute_result" 178 }, 179 { 180 "data": { 181 "image/png": "iVBORw0KGgoAAAANSUhEUgAAAQIAAAD4CAYAAAAHMeibAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjEsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy8QZhcZAAAP10lEQVR4nO3dX4wdd3nG8e/jLDEkW0OaJl5h44aAUImixAFXMUGhyJFKVKsXRrKJhKKCUByVCypElWLzJ1ERDt2bSm0Qiq9QuKBQkIEbgqW6CQYDYkUWsHJBQQISC9p6Q6WVkYwTv73YOdHx2Tl/Z878+c3zkVY7PnM8+/qc3zx+5zezcxQRmFm3bam7ADOrn4PAzBwEZuYgMDMcBGaGg8DMgIW6C+i56vprY+F1r6m7DLNkvfjc//HS2gXlrWtMECy87jXsPPVg3WWYJev5fY8PXedDAzNzEJiZg8DMcBCYGQ4CM8NBYGY4CMwMB4GZ0aALiqw5vvDomVK3d/+Ru0rdnpXPQdBRZe/ss/4sh0QzOAgSV+UOP4th9TkgquUgSEzTd/xJDf47HAzz5SBouVR2/HEcDPPlIGihruz8o/S/Bg6F4hwELVHlzn/L8rFSt/fsQ0dL3d4gh0Jxvo7AzNwRNN28OoGy/9ef9WeV3S30Xi93BtOZOQgkLQAPAz8C3gx8JiIuDzznK8DfR8QvixTZRWUGQJU7/bTyaisjHBwI0ynSETwAnIuIE5KWgIPAl3orJR0Athasr1PK2vmbvONPYrD+IsHg+YPJFAmCvcDnsuVV4G/JgkDSHcBzwNqoDUg6DBwGWNj56gKltFsZAdD2nX+U/n9bGaHgQNisSBAsAevZ8jqwHUDSdcAbI+Lfpdwbpr4sIo4DxwG27t7RuU9jLRIAKe/4o5TRLTgQNisSBGvAYra8CJzPlvcDByW9F3gL8FpJ74+IcwV+VlIcAOXpvR4OhGI068eiS3ofcHVEHM9a/IvANyPif/qe83ngkUkmC7fu3hFduJ35LCHgnX86s4RCF8Lg+X2Pc3H1XOmfa/AE8I+SDgG7gBPAY8ChAttMlgOgOrN0CV3vDmbuCMqWakcwbQB455+PaUIh1TCYV0dgIzgAmmWaLqGLpxx9ifEcOASaa9rXuiu/4OUgMDMfGpTJnUA7TDuZ2IWJRAdBSaYJAQdAM8wSCKmGgQ8NSuAQaLdp3pNU5wzcERQ06cBwADTbtGcVUusMHAQzcgCk6ZblY1OdYkwlEHxoMAOHQNpuWT428XuXyqGCO4IpOAC6ZdLDhRS6A3cEE3IIdFcXugMHwQQcApZ6GDgIxnAIWE/KYeAgGMEhYINSDQMHgZk5CIZxN2DDpNgVOAhyOARsnNTCwEEwI4eApTQGHAQDJknwlAaAFTPJWGhDV+ArC/uMe8McAJZnkisQm/6LSu4IMg4BK2rcGGlyZ+AgwCFg5WlrGDgIxnAI2LTaOGY6HQRfePTMyIRu4xtqzTBq7Iwbd3XobBA07Y2w7mnSGOxsEIzjbsCKatMY6mQQeHLQqtKWycNOBoGZXalzQeBuwKrWhq6gc0FgZpt1KgjcDVhdmt4VdCYIHAJWtyaHQWeCwMyG60QQuBuwpmhqV9CJIDCz0WYOAkkLkj4l6YCko5K29K27T9J3Jf1cUq2/hD3udwncDVjVxo27OrqCIh3BA8C5iDgB/A44CCDpVcBLEfF24JPAJwpXOQcOAKtbk8ZgkSDYC6xmy6vA/mz5EvDVbPkZYK3Azyik7lMyZrOqeuwWCYIlYD1bXge2A0TEixFxOXv8HcDysA1IOixpRdLK5bULBUqZTpOS2LqtKWOxSBCsAYvZ8iJwvn+lpJuBX0fET4ZtICKOR8SeiNiz5fprC5RiZkUUCYKTwO3Z8m3ASUk3AmTf/ywivinplb3Hq+TDAmu7KsdwkSB4Atgl6RCwCzgLPCbpGuDrwLKks8APgRcKV1qSprRiZj1NGJMz3848mwf4ePbHL2ffD2Xf31akqKLcDVgqqroNeqcuKGpC8prlqXtsJvUBJ+4ELEW9cT3PzqBTHYGZ5etMENTdepmNU+cYTSYIfFhgqZvnGE8mCEZxN2BtUddY7UQQmNloSQSBDwusK+Y11pMIAjMrJvkg8PyAtU0dYzb5IDCz8VofBJ4fsK6Zx5hvfRCM4sMCa6uqx27SQWBmk3EQmFm7g8DzA9ZVZY/9VgfBKJ4fsLarcgwnGwRmNjkHgZk5CMzMQWBmtDgIxn24qVkKqvqw1NYGgZmVx0FgZg4CM3MQmBkOAjPDQWBmtPQjz4adNvFpQ0tRb1w/+9DRTevK+pBUdwRm5iAwMweBmeEgMDMcBGaGg8DMcBCYGQWuI5C0ADwM/Ah4M/CZiLicrdsH3AoI+H5E/KCEWs1sTopcUPQAcC4iTkhaAg4CX5J0FbAM/Hn2vP8A9hUr08zmqcihwV5gNVteBfZny7uA85EBLkm6OW8Dkg5LWpG0cnntQoFSzKyIIkGwBKxny+vA9pzHB9ddISKOR8SeiNiz5fprC5RiZkUUCYI1YDFbXgTO5zw+uM7MGqhIEJwEbs+WbwNOSroxIn4G/JEywGJE/FfRQs1sfooEwRPALkmH2JgXOAs8lq07Anwk+zpSqEIzm7uZzxpkpwo/nv3xy9n3Q9m608DpYqWZWVV8QZGZOQjMzEFgZjgIzIyW3rPw/iN35d63sHdPN9+70FKSd6/CnjLuVwjuCMwMB4GZ4SAwMxwEZoaDwMxwEJgZLQ6CUadNRp1uMWuTKk4dQouDwMzK4yAwMweBmTkIzIyEg8AThtZ2VY7hVgdBmbOmZm1S9thvdRCYWTkcBGaWdhB4nsDaquqx2/og8DyBdc08xnzrg8DMiks+CHx4YG1Tx5hNPgjMbLwkgsDzBNYV8xrrSQSBmRXTiSDwPIG1RV1jNZkg8OGBpW6eYzyZIBjHXYE1XZ1jtDNBYGbDtfIjz4bptU55H4dm1lZVHPZ2qiPw4YE1Vd1jM8kg8MShpaKqsZxkEIxSd/KaDWrCmJw5CCRtk/RpSQckfThn/YckrUj6qaQ3FStzeu4KrO2qHMNFOoKPAacj4gSwJOnO3gpJu4AfR8Qe4IvApqAws+YoEgR7gdVseRXY37futxHxdLb8DLBW4OeUrgmtmBk0ZywWCYIlYD1bXge291ZExB/6nvdW4LN5G5B0ODt8WLm8dqFAKfl8eGBtVfXYHRsEku6V9NTgF7ANWMyetgicz/m7dwCnIuI3eduOiOMRsSci9my5/trZ/xUzaEoSW3c1aQyOvaAoIp4Enhx8XNIjwO3ASeA24FuSrgYWI+IFSW/Ilk9LugG4EBG/L7X6Cdx/5K6hFxj13ohblo9VWZJ13LgAqKOTLXJl4TLwsKTrgPWIeFrSXwPvlLQMfAMISQD/HRH3FC/XzOZBEVF3DQBs3b0jdp56cG7bH3fZsbsCq0Kd3cDz+x7n4uo55a3r3AVFZrZZZ4JgXNI2aeLG0tTEuYGezgQBOAysPk0OAehYEJhZvs4FgbsCq1rTuwHoYBCAw8Cq04YQgI4GgZldyUEwhLsCK6pNY6izQdCUlsy6q0ljsLNBABtvxKg3o02Jbs0yauyMG3d16HQQTMJhYNNq45hxEOCzCFaetpwlGOQgyDgMrKi2hgAk9gEnRY26dwH4/gWWb5L/JJocAuCOYJNJ3jB3B9aTQgiAg2BmDgNLaQw4CHJMmuApDQSbzqTvfRu6AXAQDOUwsGFSCwFwEJgZDoKR3BXYoBS7AXAQjOUwsJ5UQwAcBBNxGFjKIQAOgok5DLor9RAAX1k4ld4bPe4zEnwFYhq6EAA97ghm4O4gbc8+dLRTIQDuCGbm7iBNXQuAHgdBQeN+UanHgdBs03RvqYUA+NCgFNMMDB8uNE/XQwDcEZRm0s4A3B00xbShnGoIgIOgVJPOG/Q4EOrhANjMhwZm5iCYh2n/B/G8QXXcDeTzocGc+DChWTwhOJqDYM5mDQRwKBQ1S6fVxRAAB0Flpg0EcJcwKwfA9BwEFZvmNGOPu4TxisyzdD0EoEAQSNoG/AOwAtwUEf+c85xXAN+OiLfNXmJ6ZukOetwlXMkBUI4iHcHHgP+MiCcl/ZOkOyPiBwPPua/A9pNXRiD0dCUYyjjD4gDYrEgQ7AV6XcAqsB94OQgk7QPOAB8YtgFJh4HDAAs7X12glHYrEgg9KR8+lHV61QEwXJEgWALWs+V1YHtvhaTXAwsR8QtJQzcQEceB4wBbd++IArUkoX+glhUK0L5gKPO6Cu/8kxkbBJLuBT6as2obsAhcyL6f71v3buBuSR8EbpX0NeBgRFwqXnI3lNEl9OTtWE0Jh3ldTOUAmI4iZvuPWNIjwJmIOCnpGPAt4HvAYkS80Pe8pyLineO2t3X3jth56sGZaumCMgJhUmWHRJVXTjoAhnt+3+NcXD2X26IXucR4GbhH0nuA9Yh4GngXG5OIZtYiM3cEZXNHMLkqu4M2cBcwmVEdgS8oaqGyJhXbzDt/uRwELTe4Q6QaDN7x58tBkJhUgsE7frUcBIkbtkM1JSC8wzeDg6CjRu2AZYeEd/bmcxDYJt5xu8e3KjMzB4GZOQjMDAeBmeEgMDMcBGaGg8DMcBCYGQ4CM8NBYGY06MYkkv4X+FXJm/0TrryXYtO1qd421Qrtqndetf5pRNyQt6IxQTAPklYiYk/ddUyqTfW2qVZoV7111OpDAzNzEJhZ+kFwvO4CptSmettUK7Sr3sprTXqOwMwmk3pHYGYTcBCYWXpBIGmbpE9LOiDpw0Oe8wpJ36u6tjzj6pX0IUkrkn4q6U011Lcg6VNZfUclbelbty+r7+8k3Vl1bXnG1HufpO9K+rmk2u/HNqrWvud8RdJN864luSBg4yPXTkfECWBpyAC9r+KaRhlar6RdwI+zc8pfBHKDbc4eAM5l9f0OOJjVdhUbH3v3r8C/AI/WUFueYfW+CngpIt4OfBL4RH0lviy31h5JB4CtVRSSYhDsBVaz5VVgf/9KSfuAM8DFiusaZlS9v80+UxLgGWCtysIyw+rbBZyPDHBJ0s011DdoWL2XgK9my3W9loOGvveS7gCeo6I6UwyCJWA9W14HtvdWSHo9sBARv6ijsCGG1hsRf+h73luBz1ZYV8+w+vofH1xXp9x6I+LFiLicPf4ONrqZuuXWKuk64I0RsVJVIa29nbmke4GP5qzaBiwCF7Lv/ddsvxu4W9IHgVslfQ04GBGXGlpv7+/eAZyKiN/Mtch8a2zUBVfW1//44Lo6DasXgKxr+XVE/KTqwnIMq3U/cFDSe4G3AK+V9P6IODe3SiIiqS/gEeAvs+VjwF8AVwN/PPC8p+qudZJ6gTcAd2fLNwDXVFzf+4DD2fJh4G+AG7M/fwdQ9vWdul/LCeq9EfirbPmVvcebWGvfcz4P3DTvWlI8NFgG7pH0HmA9No6x38XGpFwTDa1X0nbgG8DnJJ0F/i0ifl9xfU8AuyQdYmNe4CzwWLbuCPCR7OtIxXUNk1uvpGuArwPL2Wv5Q+CF+soERr+2lfKVhWaWZEdgZlNyEJiZg8DMHARmhoPAzHAQmBkOAjPDQWBmwP8Dc3ITQlYJ4pYAAAAASUVORK5CYII=\n", 182 "text/plain": [ 183 "<Figure size 432x288 with 1 Axes>" 184 ] 185 }, 186 "metadata": {}, 187 "output_type": "display_data" 188 } 189 ], 190 "source": [ 191 "pin_univ.plot()" 192 ] 193 }, 194 { 195 "cell_type": "code", 196 "execution_count": 14, 197 "metadata": {}, 198 "outputs": [], 199 "source": [ 200 "bound_box = openmc.rectangular_prism(0.62, 0.62, boundary_type=\"reflective\")" 201 ] 202 }, 203 { 204 "cell_type": "code", 205 "execution_count": 15, 206 "metadata": {}, 207 "outputs": [], 208 "source": [ 209 "root_cell = openmc.Cell(fill=pin_univ, region=bound_box)" 210 ] 211 }, 212 { 213 "cell_type": "code", 214 "execution_count": 16, 215 "metadata": {}, 216 "outputs": [], 217 "source": [ 218 "root_univ = openmc.Universe(cells=[root_cell])" 219 ] 220 }, 221 { 222 "cell_type": "code", 223 "execution_count": 17, 224 "metadata": {}, 225 "outputs": [], 226 "source": [ 227 "geometry = openmc.Geometry(root_univ)" 228 ] 229 }, 230 { 231 "cell_type": "markdown", 232 "metadata": {}, 233 "source": [ 234 "Lastly we construct our settings. For the sake of time, a relatively low number of particles will be used." 235 ] 236 }, 237 { 238 "cell_type": "code", 239 "execution_count": 18, 240 "metadata": {}, 241 "outputs": [], 242 "source": [ 243 "settings = openmc.Settings()" 244 ] 245 }, 246 { 247 "cell_type": "code", 248 "execution_count": 19, 249 "metadata": {}, 250 "outputs": [], 251 "source": [ 252 "settings.particles = 100\n", 253 "settings.inactive = 10\n", 254 "settings.batches = 50" 255 ] 256 }, 257 { 258 "cell_type": "markdown", 259 "metadata": {}, 260 "source": [ 261 "The depletion interface relies on `OpenMC` to perform the transport simulation and obtain reaction rates and other important information. We then have to create the `xml` input files that `openmc` expects, specifically `geometry.xml`, `settings.xml`, and `materials.xml`." 262 ] 263 }, 264 { 265 "cell_type": "code", 266 "execution_count": 20, 267 "metadata": {}, 268 "outputs": [], 269 "source": [ 270 "geometry.export_to_xml()" 271 ] 272 }, 273 { 274 "cell_type": "code", 275 "execution_count": 21, 276 "metadata": {}, 277 "outputs": [], 278 "source": [ 279 "settings.export_to_xml()" 280 ] 281 }, 282 { 283 "cell_type": "markdown", 284 "metadata": {}, 285 "source": [ 286 "Before we write the material file, we must add one bit of information: the volume of our fuel. In order to translate the reaction rates obtained by `openmc` to meaningful units for depletion, we have to normalize them to a correct power. This requires us to know, or be able to calculate, how much fuel is in our problem. Correctly setting the volumes is a critical step, and can lead to incorrect answers, as the fuel is over- or under-depleted due to poor normalization.\n", 287 "\n", 288 "For our problem, we can assign the \"volume\" to be the cross-sectional area of our fuel. This is identical to modeling our fuel pin inside a box with height of 1 cm." 289 ] 290 }, 291 { 292 "cell_type": "code", 293 "execution_count": 23, 294 "metadata": {}, 295 "outputs": [], 296 "source": [ 297 "fuel.volume = math.pi * radii[0] ** 2" 298 ] 299 }, 300 { 301 "cell_type": "code", 302 "execution_count": 24, 303 "metadata": {}, 304 "outputs": [], 305 "source": [ 306 "materials.export_to_xml()" 307 ] 308 }, 309 { 310 "cell_type": "markdown", 311 "metadata": {}, 312 "source": [ 313 "## Setting up for depletion\n", 314 "\n", 315 "The OpenMC depletion interface can be accessed from the `openmc.deplete` module, and has a variety of classes that will help us." 316 ] 317 }, 318 { 319 "cell_type": "code", 320 "execution_count": 25, 321 "metadata": {}, 322 "outputs": [], 323 "source": [ 324 "import openmc.deplete" 325 ] 326 }, 327 { 328 "cell_type": "markdown", 329 "metadata": {}, 330 "source": [ 331 "In order to run the depletion calculation we need the following information:\n", 332 "\n", 333 "1. Nuclide decay, fission yield, and reaction data\n", 334 "2. Operational power or power density\n", 335 "3. Desired depletion schedule\n", 336 "4. Desired time integration scheme\n", 337 "\n", 338 "The first item is necessary to determine the paths by which nuclides transmute over the depletion simulation. This includes spontaneous decay, fission product yield distributions, and nuclides produced through neutron-reactions. For example,\n", 339 "* Te129 decays to I129 with a half life of ~70 minutes\n", 340 "* A fission event for U-235 produces fission products like Xe135 according to a distribution\n", 341 "* For thermal problems, Am241 will produce metastable Am242 about 8% of the time during an $(n,\\gamma)$ reaction. The other 92% of capture reactions will produce ground state Am242\n", 342 "\n", 343 "These data are often distributed with other nuclear data, like incident neutron cross sections with ENDF/B-VII.\n", 344 "OpenMC uses the [`openmc.deplete.Chain`](https://docs.openmc.org/en/latest/pythonapi/generated/openmc.deplete.Chain.html#openmc.deplete.Chain) to collect represent the various decay and transmutation pathways in a single object.\n", 345 "While a complete `Chain` can be created using nuclear data files, users may prefer to download pre-generated XML-representations instead.\n", 346 "Such files can be found at https://openmc.org/depletion-chains/ and include full and compressed chains, with capture branching ratios derived using PWR- or SFR-spectra.\n", 347 "\n", 348 "For this problem, we will be using a much smaller depletion chain that contains very few nuclides. In a realistic problem, over 1000 isotopes may be included in the depletion chain." 349 ] 350 }, 351 { 352 "cell_type": "code", 353 "execution_count": 26, 354 "metadata": {}, 355 "outputs": [], 356 "source": [ 357 "chain = openmc.deplete.Chain.from_xml(\"./chain_simple.xml\")" 358 ] 359 }, 360 { 361 "cell_type": "code", 362 "execution_count": 27, 363 "metadata": {}, 364 "outputs": [ 365 { 366 "data": { 367 "text/plain": [ 368 "OrderedDict([('I135', 0),\n", 369 " ('Xe135', 1),\n", 370 " ('Xe136', 2),\n", 371 " ('Cs135', 3),\n", 372 " ('Gd157', 4),\n", 373 " ('Gd156', 5),\n", 374 " ('U234', 6),\n", 375 " ('U235', 7),\n", 376 " ('U238', 8)])" 377 ] 378 }, 379 "execution_count": 27, 380 "metadata": {}, 381 "output_type": "execute_result" 382 } 383 ], 384 "source": [ 385 "chain.nuclide_dict" 386 ] 387 }, 388 { 389 "cell_type": "markdown", 390 "metadata": {}, 391 "source": [ 392 "The primary entry point for depletion is the `openmc.deplete.Operator`. It relies on the `openmc.deplete.Chain` and helper classes to run `openmc`, retrieve and normalize reaction rates, and other perform other tasks. For a thorough description, please see the full API documentation." 393 ] 394 }, 395 { 396 "cell_type": "markdown", 397 "metadata": {}, 398 "source": [ 399 "We will create our Operator using the geometry and settings from above, and our simple chain file. The materials are read in automatically using the `materials.xml` file." 400 ] 401 }, 402 { 403 "cell_type": "code", 404 "execution_count": 28, 405 "metadata": {}, 406 "outputs": [], 407 "source": [ 408 "operator = openmc.deplete.Operator(geometry, settings, \"./chain_simple.xml\")" 409 ] 410 }, 411 { 412 "cell_type": "markdown", 413 "metadata": {}, 414 "source": [ 415 "We will then simulate our fuel pin operating at linear power of 174 W/cm, or 174 W given a unit height for our problem." 416 ] 417 }, 418 { 419 "cell_type": "code", 420 "execution_count": 29, 421 "metadata": {}, 422 "outputs": [], 423 "source": [ 424 "power = 174" 425 ] 426 }, 427 { 428 "cell_type": "markdown", 429 "metadata": {}, 430 "source": [ 431 "For this problem, we will take depletion step sizes of 30 days, and instruct OpenMC to re-run a transport simulation every 30 days until we have modeled the problem over a six month cycle. The depletion interface expects the time to be given in seconds, so we will have to convert. Note that these values are not cumulative." 432 ] 433 }, 434 { 435 "cell_type": "code", 436 "execution_count": 30, 437 "metadata": {}, 438 "outputs": [], 439 "source": [ 440 "time_steps = [30 * 24 * 60 * 60] * 6" 441 ] 442 }, 443 { 444 "cell_type": "markdown", 445 "metadata": {}, 446 "source": [ 447 "And lastly, we will use the basic predictor, or forward Euler, time integration scheme. Other, more advanced methods are provided to the user through `openmc.deplete`" 448 ] 449 }, 450 { 451 "cell_type": "code", 452 "execution_count": 31, 453 "metadata": {}, 454 "outputs": [], 455 "source": [ 456 "integrator = openmc.deplete.PredictorIntegrator(operator, time_steps, power)" 457 ] 458 }, 459 { 460 "cell_type": "markdown", 461 "metadata": {}, 462 "source": [ 463 "To perform the simulation, we use the `integrate` method, and let `openmc` take care of the rest." 464 ] 465 }, 466 { 467 "cell_type": "code", 468 "execution_count": 32, 469 "metadata": {}, 470 "outputs": [], 471 "source": [ 472 "integrator.integrate()" 473 ] 474 }, 475 { 476 "cell_type": "markdown", 477 "metadata": {}, 478 "source": [ 479 "## Processing the outputs\n", 480 "\n", 481 "The depletion simulation produces a few output files. First, the statepoint files from each individual transport simulation are written to `openmc_simulation_n<N>.h5`, where `<N>` indicates the current depletion step. Any tallies that we defined in `tallies.xml` will be included in these files across our simulations. We have 7 such files, one for each our of 6 depletion steps and the initial state." 482 ] 483 }, 484 { 485 "cell_type": "code", 486 "execution_count": 33, 487 "metadata": {}, 488 "outputs": [ 489 { 490 "name": "stdout", 491 "output_type": "stream", 492 "text": [ 493 "c5g7.h5\t\t\t openmc_simulation_n2.h5 openmc_simulation_n6.h5\r\n", 494 "depletion_results.h5\t openmc_simulation_n3.h5 statepoint.50.h5\r\n", 495 "openmc_simulation_n0.h5 openmc_simulation_n4.h5 summary.h5\r\n", 496 "openmc_simulation_n1.h5 openmc_simulation_n5.h5\r\n" 497 ] 498 } 499 ], 500 "source": [ 501 "!ls *.h5" 502 ] 503 }, 504 { 505 "cell_type": "markdown", 506 "metadata": {}, 507 "source": [ 508 "The `depletion_results.h5` file contains information that is aggregated over all time steps through depletion. This includes the multiplication factor, as well as concentrations. We can process this file using the `openmc.deplete.ResultsList` object" 509 ] 510 }, 511 { 512 "cell_type": "code", 513 "execution_count": 34, 514 "metadata": {}, 515 "outputs": [], 516 "source": [ 517 "results = openmc.deplete.ResultsList.from_hdf5(\"./depletion_results.h5\")" 518 ] 519 }, 520 { 521 "cell_type": "code", 522 "execution_count": 35, 523 "metadata": {}, 524 "outputs": [], 525 "source": [ 526 "time, k = results.get_eigenvalue()" 527 ] 528 }, 529 { 530 "cell_type": "code", 531 "execution_count": 36, 532 "metadata": {}, 533 "outputs": [], 534 "source": [ 535 "time /= (24 * 60 * 60) # convert back to days from seconds" 536 ] 537 }, 538 { 539 "cell_type": "code", 540 "execution_count": 37, 541 "metadata": {}, 542 "outputs": [ 543 { 544 "data": { 545 "text/plain": [ 546 "array([[0.76882937, 0.00982155],\n", 547 " [0.75724033, 0.00827689],\n", 548 " [0.75532242, 0.01031746],\n", 549 " [0.74796855, 0.00919769],\n", 550 " [0.74066561, 0.01157708],\n", 551 " [0.73184492, 0.00971504],\n", 552 " [0.7207293 , 0.00703074]])" 553 ] 554 }, 555 "execution_count": 37, 556 "metadata": {}, 557 "output_type": "execute_result" 558 } 559 ], 560 "source": [ 561 "k" 562 ] 563 }, 564 { 565 "cell_type": "markdown", 566 "metadata": {}, 567 "source": [ 568 "The first column of `k` is the value of `k-combined` at each point in our simulation, while the second column contains the associated uncertainty. We can plot this using `matplotlib`" 569 ] 570 }, 571 { 572 "cell_type": "code", 573 "execution_count": 38, 574 "metadata": {}, 575 "outputs": [], 576 "source": [ 577 "from matplotlib import pyplot" 578 ] 579 }, 580 { 581 "cell_type": "code", 582 "execution_count": 39, 583 "metadata": {}, 584 "outputs": [ 585 { 586 "data": { 587 "image/png": "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\n", 588 "text/plain": [ 589 "<Figure size 432x288 with 1 Axes>" 590 ] 591 }, 592 "metadata": {}, 593 "output_type": "display_data" 594 } 595 ], 596 "source": [ 597 "pyplot.errorbar(time, k[:, 0], yerr=k[:, 1])\n", 598 "pyplot.xlabel(\"Time [d]\")\n", 599 "pyplot.ylabel(\"$k_{eff}\\pm \\sigma$\");" 600 ] 601 }, 602 { 603 "cell_type": "markdown", 604 "metadata": {}, 605 "source": [ 606 "Due to the low number of particles selected, we have not only a very high uncertainty, but likely a horrendously poor fission source. This pin cell should have $k>1$, but we can still see the decline over time due to fuel consumption." 607 ] 608 }, 609 { 610 "cell_type": "markdown", 611 "metadata": {}, 612 "source": [ 613 "We can then examine concentrations of atoms in each of our materials. This requires knowing the material ID, which can be obtained from the `materials.xml` file." 614 ] 615 }, 616 { 617 "cell_type": "code", 618 "execution_count": 40, 619 "metadata": {}, 620 "outputs": [], 621 "source": [ 622 "_time, u5 = results.get_atoms(\"1\", \"U235\")\n", 623 "_time, xe135 = results.get_atoms(\"1\", \"Xe135\")" 624 ] 625 }, 626 { 627 "cell_type": "code", 628 "execution_count": 41, 629 "metadata": {}, 630 "outputs": [ 631 { 632 "data": { 633 "image/png": "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\n", 634 "text/plain": [ 635 "<Figure size 432x288 with 1 Axes>" 636 ] 637 }, 638 "metadata": {}, 639 "output_type": "display_data" 640 } 641 ], 642 "source": [ 643 "pyplot.plot(time, u5, label=\"U235\")\n", 644 "pyplot.xlabel(\"Time [d]\")\n", 645 "pyplot.ylabel(\"Number of atoms - U235\");" 646 ] 647 }, 648 { 649 "cell_type": "code", 650 "execution_count": 42, 651 "metadata": {}, 652 "outputs": [ 653 { 654 "data": { 655 "image/png": "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\n", 656 "text/plain": [ 657 "<Figure size 432x288 with 1 Axes>" 658 ] 659 }, 660 "metadata": {}, 661 "output_type": "display_data" 662 } 663 ], 664 "source": [ 665 "pyplot.plot(time, xe135, label=\"Xe135\")\n", 666 "pyplot.xlabel(\"Time [d]\")\n", 667 "pyplot.ylabel(\"Number of atoms - Xe135\");" 668 ] 669 }, 670 { 671 "cell_type": "markdown", 672 "metadata": {}, 673 "source": [ 674 "We can also examine reaction rates over time using the `ResultsList`" 675 ] 676 }, 677 { 678 "cell_type": "code", 679 "execution_count": 43, 680 "metadata": {}, 681 "outputs": [], 682 "source": [ 683 "_time, u5_fission = results.get_reaction_rate(\"1\", \"U235\", \"fission\")" 684 ] 685 }, 686 { 687 "cell_type": "code", 688 "execution_count": 44, 689 "metadata": {}, 690 "outputs": [ 691 { 692 "data": { 693 "image/png": "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\n", 694 "text/plain": [ 695 "<Figure size 432x288 with 1 Axes>" 696 ] 697 }, 698 "metadata": {}, 699 "output_type": "display_data" 700 } 701 ], 702 "source": [ 703 "pyplot.plot(time, u5_fission)\n", 704 "pyplot.xlabel(\"Time [d]\")\n", 705 "pyplot.ylabel(\"Fission reactions / s\");" 706 ] 707 }, 708 { 709 "cell_type": "markdown", 710 "metadata": {}, 711 "source": [ 712 "## Helpful tips\n", 713 "\n", 714 "Depletion is a tricky task to get correct. Use too short of time steps and you may never get your results due to running many transport simulations. Use long of time steps and you may get incorrect answers. Consider the xenon plot from above. Xenon-135 is a fission product with a thermal absorption cross section on the order of millions of barns, but has a half life of ~9 hours. Taking smaller time steps at the beginning of your simulation to build up some equilibrium in your fission products is highly recommended.\n", 715 "\n", 716 "When possible, differentiate materials that reappear in multiple places. If we had built an entire core with the single `fuel` material, every pin would be depleted using the same averaged spectrum and reaction rates which is incorrect. The `Operator` can differentiate these materials using the `diff_burnable_mats` argument, but note that the volumes will be copied from the original material.\n", 717 "\n", 718 "Using higher-order integrators, like the `CECMIntegrator`, `EPCRK4Integrator` with a fourth order Runge-Kutta, or the `LEQIIntegrator`, can improve the accuracy of a simulation, or at least allow you to take longer depletion steps between transport simulations with similar accuracy.\n", 719 "\n", 720 "Fuel pins with integrated burnable absorbers, like gadolinia, experience strong flux gradients until the absorbers are mostly burned away. This means that the spectrum and magnitude of the flux at the edge of the fuel pin can be vastly different than that in the interior. The helper `pin` function can be used to subdivide regions into equal volume segments, as follows." 721 ] 722 }, 723 { 724 "cell_type": "code", 725 "execution_count": 45, 726 "metadata": {}, 727 "outputs": [], 728 "source": [ 729 "div_surfs_1 = [openmc.ZCylinder(r=1)]\n", 730 "div_1 = openmc.model.pin(div_surfs_1, [fuel, water], subdivisions={0: 10})" 731 ] 732 }, 733 { 734 "cell_type": "code", 735 "execution_count": 46, 736 "metadata": {}, 737 "outputs": [ 738 { 739 "data": { 740 "text/plain": [ 741 "<matplotlib.image.AxesImage at 0x7f9ae8572a90>" 742 ] 743 }, 744 "execution_count": 46, 745 "metadata": {}, 746 "output_type": "execute_result" 747 }, 748 { 749 "data": { 750 "image/png": "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\n", 751 "text/plain": [ 752 "<Figure size 432x288 with 1 Axes>" 753 ] 754 }, 755 "metadata": {}, 756 "output_type": "display_data" 757 } 758 ], 759 "source": [ 760 "div_1.plot(width=(2.0, 2.0))" 761 ] 762 }, 763 { 764 "cell_type": "markdown", 765 "metadata": {}, 766 "source": [ 767 "The innermost region has been divided into 10 equal volume regions. We can pass additional arguments to divide multiple regions, except for the region outside the last cylinder." 768 ] 769 }, 770 { 771 "cell_type": "markdown", 772 "metadata": {}, 773 "source": [ 774 "## Register depletion chain\n", 775 "\n", 776 "The depletion chain we created can be registered into the OpenMC `cross_sections.xml` file, so we don't have to always pass the `chain_file` argument to the `Operator`. To do this, we create a `DataLibrary` using `openmc.data`. Without any arguments, the `from_xml` method will look for the file located at `OPENMC_CROSS_SECTIONS`. For this example, we will just create a bare library." 777 ] 778 }, 779 { 780 "cell_type": "code", 781 "execution_count": 47, 782 "metadata": {}, 783 "outputs": [], 784 "source": [ 785 "data_lib = openmc.data.DataLibrary()" 786 ] 787 }, 788 { 789 "cell_type": "code", 790 "execution_count": 48, 791 "metadata": {}, 792 "outputs": [], 793 "source": [ 794 "data_lib.register_file(\"./chain_simple.xml\")" 795 ] 796 }, 797 { 798 "cell_type": "code", 799 "execution_count": 49, 800 "metadata": {}, 801 "outputs": [], 802 "source": [ 803 "data_lib.export_to_xml()" 804 ] 805 }, 806 { 807 "cell_type": "code", 808 "execution_count": 50, 809 "metadata": {}, 810 "outputs": [ 811 { 812 "name": "stdout", 813 "output_type": "stream", 814 "text": [ 815 "<?xml version='1.0' encoding='utf-8'?>\r\n", 816 "<cross_sections>\r\n", 817 " <depletion_chain path=\"chain_simple.xml\" type=\"depletion_chain\" />\r\n", 818 "</cross_sections>\r\n" 819 ] 820 } 821 ], 822 "source": [ 823 "!cat cross_sections.xml" 824 ] 825 }, 826 { 827 "cell_type": "markdown", 828 "metadata": {}, 829 "source": [ 830 "This allows us to make an `Operator` simply with the geometry and settings arguments, provided we exported our library to `OPENMC_CROSS_SECTIONS`. For a problem where we built and registered a `Chain` using all the available nuclear data, we might see something like the following." 831 ] 832 }, 833 { 834 "cell_type": "code", 835 "execution_count": 51, 836 "metadata": {}, 837 "outputs": [], 838 "source": [ 839 "new_op = openmc.deplete.Operator(geometry, settings)" 840 ] 841 }, 842 { 843 "cell_type": "code", 844 "execution_count": 52, 845 "metadata": {}, 846 "outputs": [ 847 { 848 "data": { 849 "text/plain": [ 850 "3820" 851 ] 852 }, 853 "execution_count": 52, 854 "metadata": {}, 855 "output_type": "execute_result" 856 } 857 ], 858 "source": [ 859 "len(new_op.chain.nuclide_dict)" 860 ] 861 }, 862 { 863 "cell_type": "code", 864 "execution_count": 53, 865 "metadata": {}, 866 "outputs": [ 867 { 868 "data": { 869 "text/plain": [ 870 "['H1', 'H2', 'H3', 'H4', 'H5', 'H6', 'H7', 'He3', 'He4', 'He5']" 871 ] 872 }, 873 "execution_count": 53, 874 "metadata": {}, 875 "output_type": "execute_result" 876 } 877 ], 878 "source": [ 879 "[nuc.name for nuc in new_op.chain.nuclides[:10]]" 880 ] 881 }, 882 { 883 "cell_type": "code", 884 "execution_count": 54, 885 "metadata": {}, 886 "outputs": [ 887 { 888 "data": { 889 "text/plain": [ 890 "['Ds268',\n", 891 " 'Ds269',\n", 892 " 'Ds270',\n", 893 " 'Ds270_m1',\n", 894 " 'Ds271',\n", 895 " 'Ds271_m1',\n", 896 " 'Ds272',\n", 897 " 'Ds273',\n", 898 " 'Ds279_m1',\n", 899 " 'Rg272']" 900 ] 901 }, 902 "execution_count": 54, 903 "metadata": {}, 904 "output_type": "execute_result" 905 } 906 ], 907 "source": [ 908 "[nuc.name for nuc in new_op.chain.nuclides[-10:]]" 909 ] 910 }, 911 { 912 "cell_type": "markdown", 913 "metadata": {}, 914 "source": [ 915 "## Choice of depletion step size\n", 916 "\n", 917 "A general rule of thumb is to use depletion step sizes around 2 MWd/kgHM, where kgHM is really the initial heavy metal mass in kg. If your problem includes integral burnable absorbers, these typically require shorter time steps at or below 1 MWd/kgHM. These are typically valid for the predictor scheme, as the point of recent schemes is to extend this step size. A good convergence study, where the step size is decreased until some convergence metric is satisfied, is a beneficial exercise.\n", 918 "\n", 919 "We can use the `Operator` to determine our maximum step size using this recommendation. The `heavy_metal` attribute returns the mass of initial heavy metal in g, which, using our power, can be used to compute this step size. $$\\frac{2\\,MWd}{kgHM} = \\frac{P\\times\\Delta}{hm_{op}}$$" 920 ] 921 }, 922 { 923 "cell_type": "code", 924 "execution_count": 55, 925 "metadata": {}, 926 "outputs": [ 927 { 928 "data": { 929 "text/plain": [ 930 "5.080339195584719" 931 ] 932 }, 933 "execution_count": 55, 934 "metadata": {}, 935 "output_type": "execute_result" 936 } 937 ], 938 "source": [ 939 "operator.heavy_metal" 940 ] 941 }, 942 { 943 "cell_type": "code", 944 "execution_count": 56, 945 "metadata": {}, 946 "outputs": [], 947 "source": [ 948 "max_step = 2 * operator.heavy_metal / power * 1E3" 949 ] 950 }, 951 { 952 "cell_type": "code", 953 "execution_count": 57, 954 "metadata": {}, 955 "outputs": [ 956 { 957 "name": "stdout", 958 "output_type": "stream", 959 "text": [ 960 "\"Maximum\" depletion step: 58.4 [d]\n" 961 ] 962 } 963 ], 964 "source": [ 965 "print(\"\\\"Maximum\\\" depletion step: {:5.3} [d]\".format(max_step))" 966 ] 967 }, 968 { 969 "cell_type": "markdown", 970 "metadata": {}, 971 "source": [ 972 "Alternatively, if we were provided the power density of our problem, we can provide this directly with `openmc.deplete.PredictorIntegrator(operator, time_steps, power_density=pdens)`. The values of `power` and `power_density` do not have to be scalars. For problems with variable power, we can provide an iterable with the same number of elements as `time_steps`." 973 ] 974 } 975 ], 976 "metadata": { 977 "kernelspec": { 978 "display_name": "Python 3", 979 "language": "python", 980 "name": "python3" 981 }, 982 "language_info": { 983 "codemirror_mode": { 984 "name": "ipython", 985 "version": 3 986 }, 987 "file_extension": ".py", 988 "mimetype": "text/x-python", 989 "name": "python", 990 "nbconvert_exporter": "python", 991 "pygments_lexer": "ipython3", 992 "version": "3.8.3" 993 } 994 }, 995 "nbformat": 4, 996 "nbformat_minor": 2 997} 998