Research on the perturbation phenomenon while tracing the radon concentration in real time

Abstract

Generally, researchers are interested in time averaged radon concentration levels. However when we study the migration and adsorption characteristics of radon, the measurement of radon concentration in real time is important. Radon monitors based on electrostatic collection method cannot follow the rapid changes in radon concentration. The main reason for this is that a sufficient decay time is needed in order for the radon concentration in the internal cell of radon monitor to come to equilibrium with the ²¹⁸Po. We propose a novel algorithm for determining the actual radon concentration versus time, derived from the data provided by the radon monitor. However there is a distinct ‘perturbation’ phenomenon associated with this procedure when the measurement cycle time is short. In this paper we will also analyze the source of this perturbation phenomenon and provide an improved process model, based upon a faster convergence method that enables reduction of this perturbation to acceptable limits. This model can be used to improve the measurements for any radon monitor like Rad7 based on electrostatic collection for tracing the radon concentration on short measurement cycles.

Appendix: Physics base of Eqs. (6) and (8)

For example, the radon atom number in the internal cell of the RAD7 is N, and it is approximate a constant for the long half life.

Then,

$$ \frac{dN}{dt} = - \lambda N $$

(29)

where $\lambda$ is the radon decay constant.

The Po-218 atom number in the internal cell of the RAD7 is Np, then,

$$ \frac{{dN_{P} (t)}}{dt} = \lambda N - \lambda_{P} N_{P} (t) $$

(30)

where $\lambda_{P}$ is the Po-218 decay constant.

Two side of Eq. (30) multiply $\lambda_{P}$, and

$$ A_{R} = \lambda N $$

(31)

$$ A_{P} (t) = \lambda_{P} N_{P} (t) $$

(32)

where $A_{R}$, $A_{P} (t)$ are the radon and Po-218 activity in the internal cell of radon monitor, respectively.

Equation (30) can be rewritten as:

$$ \frac{{dA_{P} (t)}}{dt} = \lambda_{P} A_{R} - \lambda_{P} A_{P} (t) $$

(33)

According the definition of activity concentration, two side of Eq. (33) are divided by V (the volume of the internal cell), then,

$$ \frac{{dC_{P} (t)}}{dt} = \lambda_{P} C_{R} - \lambda_{P} C_{P} (t) $$

(34)

This is the physics base of Eqs. (6) and (8).