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Determination of the exhalation-rate (Flux)

General information

During an exhalation measurement the values of radon will increase over the time because of physical properties of decay as long as there is no saturation in the detection chamber. For the evaluation of the exhalation rate a calculation program ERSEval (Data view 190 kB and Chart view 110 kB) was designed that covers the ranges of low and high exhalation rates. Over selected values an average slope can be determined by linear fit as the established method. Especially at lower exhalation- and higher chamber ventilation rates the linear fit fails and delivers too low exhalation rates. In this case an exponential fit is recommended that numerically determines the variables of the exponential growth.

Sample spectrum

Typical sample spectrum

Linear fit calculation

Linear regression leads to the equation:

C(t) = Slope · t + Intercept (Linear-function)

with C(t) as a function of t (time). The two constants Slope and Intercept will be calculated so that square of deviation is a minimum.

The constant Slope is the average slope and necessary to calculate the exhalation-rate (Flux).

Evaluation of flux by linear fit

Evaluation of flux by linear fit

Geometric constants

Volume of a half-sphere with D = 160 mm is V = 0.00155 m
Surface of a half-sphere with D = 160 mm is A = 0.02009 m

With the measuring interval t[s] and the average Slope the exhalation rate (Flux) F can be determined to:

F = Slope · V / A [Bq/m²s]

Exponential fit calculation

Exponential regression leads to the equation:

C(t) = Cmax · (1-exp-(l · t)) (Exponential growth)

with Cmax as saturation or plateau concentration and l as sum of radon decay constant lRn and ventilation rate lv. This equation contains the two unknown variables Cmax and lv.

By a numerical iteration process the ventilation rate of the chamber lv can be determined with good accuracy as well as the saturation concentration to calculate the exponential fit by the least squares method.

Evaluation of flux by exponential fit

Evaluation of flux by exponential fit

With the calculated values exhalation rate (Flux) F can be determined to:

F = Cmax · l ·V / A [Bq/m²s]