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STELLA model for Radon Progeny Collection

This appendix is included to give interested readers of the paper A comparison of electrostatic and filtered air collection of radon progeny (Eur. J. phys 25 (2004) 239-248), who may not be familiar with STELLA [14], a rudimentary feel for the utility of the STELLA modeling program.

The analytic solutions given in section 3 of the above mentioned paper are useful, and were used to fit experiment to theory. However, the modeling program STELLA, which can be used to solve differential equations numerically, and in particular the rate equations for the Radon progeny, proves to be a more effective tool for testing various collection scenarios in a reasonable amount of time. In the above mentioned paper we have used STELLA to generate the theoretical activity ratio of Bi214 to Pb214 at 15 minutes after sampling ends. These are then compared to experiment (see Figure 4 of the above mentioned paper).

STELLA is an icon based, systems modeling program, which, in its basic form, uses four icons (called Stocks, Flows, Converters and Connectors) to model complex systems. Figure A1 shows the STELLA model used to model the decay of Radon progeny.

Figure A1

In Figure A1, we have shown the basic icons (Stocks, Flows and Converters) to the upper left of the model and labeled them accordingly. The icon for the Connector is not shown because it cannot stand alone. These examples of the icons are not part of the model. The icons are obtained from the bar beneath the top menu bar (see Figure A1) by clicking and dragging the icon of interest and placing it in position on the model page. Inspection shows, that the model we have constructed mimics the structure of the standard decay scheme shown in Figure 1 of the above mentioned paper. In the model in Figure A1, the Flows control the activities of the progeny. The collection of progeny is controlled by the Converter labeled “Collection” and the Flows labeled f1, f2, and f3. The activities from Stocks corresponding to progeny Pb214 and Bi214 are Connected to a Converter labeled Total count.  This is the total beta activity. The Converter R close to the Total count calculates the ratio (Activity Bi214/Activity Pb214). Any, and/or all of the labeled variables can be tabulated and/or plotted. The data can also be copied and transferred to other spread sheet programs if desired. As the model is constructed a program is generated on the program page. The user can toggle between the model page and the program page by clicking on the up and down arrowheads at the top of the left hand vertical bar. All that the user must do is enter the initial conditions and any other controlling parameters by clicking on the relevant program line. Initially, the lines requiring attention of this kind appear with a question mark to the left of the relevant line.  Figure A2 shows the completed program page.

Figure A2

Secular equilibrium is assumed for the distribution of Radon progeny for the particular page shown. For secular equilibrium the concentration ratios of   Po218: Pb214: Bi214 are 1:8.636:6.427.  This is reflected in the program lines for f1, f2 and f3.  The parameter “Collection” determines how the collection rate varies with time and is entered graphically for our particular model. Potentially, this enables us to investigate time varying collection scenarios if we so choose. Once the model and program have been set up the model can be run. The user can choose the numerical method to be used (Euler, Runge-Kutta 2 or Runge- Kutta 4), the step size and the integration length. We have used the fourth order Runga-Kutta option with a step size of 0.1 min and a run time of 200 minutes.

An example of the activity curves that are generated by the above model is shown in Figure A3.

Figure A3

            Figure A3 shows the activities of Po218, Pb214 and Bi214 , and the total beta activity for a thirty minute progeny collection time assuming secular equilibrium. Figure A4 shows the same progeny activity curves for the same collection time but assumes that only Po218 is collected.

Figure A4

Comparison of Figures A3 and A4,  show distinct differences in the activity curves for the two different collection scenarios.

            The model described above is quite useful in generating large amounts of comparative data. The ability to do this may be helpful in devising alternative methods  for establishing the relative concentrations of progeny collected by various means.