Radioactive Decay and Dose

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In this section we're going to pretend the release consisted of radioactive particles which decay and deposit. The air concentration and deposition amounts will be converted to dose. Although we will try to make some reasonable assumptions, this is still a simplistic example of what can be a complex modeling problem. The details presented here should just be used as an example in configuring the model and not as a template for simulating a nuclear accident.

  1. The decay of radioactive pollutants is treated the same way as transformation and deposition. The mass on a particle is reduced using the time constant approach:
    • m2 = m1 exp(-βrad Δt)

    In addition to the particle mass, deposited radioactive pollutants also decay, and hence deposition amounts are also reduced each time step. The decay constant for radioactive processes is defined by the half-life (T½):
    • βrad = ln 2 / T½

  2. For the purposes of this example, we will assume a release from a hypothetical nuclear reactor located at the CAPTEX release point, essentially the same configuration we have been using for all the previous examples. Start by retrieving the saved captex_control.txt and captex_setup.txt settings into the GUI menu. We will assume that a 3000 MW (thermal) reactor that has been running for one year creates about1.0E+17 Bq of Cesium-137 (and many other fission products). We also assume that 10% of the Cesium is released in the accident over a one-hour period.

  3. To configure this release, set the run duration to 25 h, open the Setup Run / Pollutant menu and enter the C137 label, release amount 1.0E+16, and the 1.0 hour duration. Save the changes and open the Setup Run / Grid menu and change the name of the output file to c137.bin, and add the second level 0 for deposition. Then open the Setup Run / Deposition menu and check the Cs-137 radio-button to set the deposition defaults for Cesium. Save the changes and then run the model.

  4. To convert the air concentration and ground deposition values into a number that can be more easily be related to health effects, we need to find the dose conversion factors for Cesium-137. For the airborne plume assume 3.4E-11 (REM/hr) / (Bq/m3) and 1.1E-12 (REM/hr) / (Bq/m2) for the deposited material. Because the air concentrations are three-hour averages, the air concentration dose conversion factor will be 1.0E-10 and if we compute the total deposition over 24 hours, then the deposition dose conversion factor becomes 2.6E-11. Open the Display / Contours menu and enter the dose conversion factors. Before executing the display, the plot labels should be modified to reflect the changes. Just changing the units field in the menu to REM is insufficient because it will incorrectly show as REM/m3.

  5. To make more complex changes to the graphics label, open the Configuration Setup / Border Labels menu and enter Cesium 137 for a new plot title, Dose Equivalent for the map type, and REM for the mass units into their respective text entry fields. Leave the other fields blank. Then save the changes and go back and execute the Contour Display menu and advance the frames to the end to see the one-day accumulated ground-shine dose map.

  6. Because Cesium has such a long-half life, the deposited material will continue to be a problem for quite some time. The decay after one year is so small that we can compute the one-year ground-shine by multiplying the dose conversion factor by 8760 rather than 24 (9.6E-09). The accumulated dose becomes 365 times larger. The conversion factor could also be adjusted for the actual Cesium decay.

The example presented here was intended show the model can be configured for a radiological simulation. The emission and dose conversion values are only intended as examples and a guideline for an actual accident scenario, which is composed of a complex mix of short- and long-lived radionuclides. Other radiological simulations could also be configured with the model, but their complexity is beyond the scope of this tutorial. Although there are many public sites with radiological monitoring data, frequently these sites only show background values, except when there has been some event.