A periodic pumping technique of soil gas for ²²²Rn stabilization in large calibration chambers: part 2-theoretical...

In an adjoining publication, we demonstrated the novel technique to harvest soil gas of natural origin as a highly efficient source of ²²²Rn for calibration applications in a large volume ²²²Rn calibration chamber. Its advantages over the use of conventional high strength ²²⁶Ra sources, such as the capability to serve as a non-depleting reservoir of ²²²Rn and achieve the desired concentration inside the calibration chamber within a very short time, devoid of radiation safety issues in source handling and licensing requirements from the regulatory authority, were discussed in detail. It was also demonstrated that stability in the ²²²Rn concentration in large calibration chambers could be achieved within ± 20% deviation from the desired value through a semi-dynamic mode of injection in which ²²²Rn laden air was periodically pumped to compensate for its loss due to leak and decay. The necessity of developing a theory for determining the appropriate periodicity of pumping was realized to get good temporal stability with a universally acceptable deviation of ≤ ± 10% in the ²²²Rn concentration. In this paper, we present a mathematical formulation to determine the injection periods (injection pump ON and OFF durations) for the semi-dynamic operation to achieve long term temporal stability in the ²²²Rn concentration in the chamber. These computed pumping parameters were then used to efficiently direct the injection of soil gas into the chamber. We present the mathematical formulation, and its experimental validations in a large volume calibration chamber (22 m³). With this, the temporal stability of ²²²Rn concentration in the chamber was achieved with a deviation of ~ 3% from the desired value.