Answer to Question #1787 Submitted to "Ask the Experts"

Q

Are there any algorithms in the literature for calculating (or approximating) radioactive emissions from stacks, for both continuous flow samplers and periodic sampling? A reference and/or the actual algorithm would be great. I can find details on the details, but nothing yet on a standard formulae. For your general information, I have come across two different unpublished methods that contractors at one facility use to calculate the release from stacks, with very little documentation attached. (The variables [such as line losses] and conversion factors were pretty well documented. For brevity, I do not include that information here. Factors to convert units were also included).

1. I assume this one was for continuous sampling: Curies = ave concentration * ave stack flow rate/correction factor
    
2. I assume this one was for periodic sampling: Curies = (Sample activity * stack flow rate/sampler flow rate * duration of emission/duration of sample)/(post-lab correction factor * sampler operation efficiency factor * transport efficiency factor * collection media efficiency factor)

Thank you. I'm stumped.

A

The short answer is no, there are no standard formulae. The calculations are fairly easy however. To begin with, these calculations would be the same for continuous sampling and periodic sampling. The only difference, if it can be called that, is that in the latter case we assume that the concentration in the stack when the sample is collected is no different than the concentration during the time we are not sampling. Continuous sampling simply avoids this assumption because there are no periods during which a sample is not being collected. Periodic sampling is usually employed when the concentrations in the effluent are so low that any potential dose (including that of an accidental release) to the public would be a very small fraction of the allowable levels. In such a case, the errors introduced by temporal variations in the concentrations would be of little consequence. There are many equivalent ways to perform the calculation. To make the examples more understandable, we will employ an arbitrary set of units:

Q = C x v x A, where

Q, the release rate from the stack, is in units of µCi/minute

C, the measured concentration in the sample, is in units of µCi/cubic centimeter

v, the average velocity of the stack effluents, is in units of centimeters/minute

A, the cross sectional area of the stack, is in square centimeters

This could also be written Q = C x F(stack) where F(stack) is the volumetric flow rate of the effluent in the stack in ml/minute. The above equations could be multiplied or divided by an appropriate correction factor to account for any losses of particulates or iodine in the sample lines. Alternatively, the line loss correction could be employed in the calculation of C. Explaining the equations used by continuous real-time monitors to calculate the concentration in the sampled effluent is too lengthy an endeavor for an ATE question/answer. Hence we assume that particulates are collected on a filter over a specified sampling time t (in minutes), or iodine is collected on charcoal and the sample is then counted in the laboratory. If the half-life of the radionuclide is long compared to the sample time, the measured concentration (µCi/ml) is:

C = A/(V x E) = A/(F x t x E)

In this case A is the measured activity on the filter or in the charcoal in µCi, not the area of the stack as in the first equation.

V is the volume of the sampled effluent in ml

E is the collection media efficiency (often 1 for a particulate filter)

F is the sample flow rate through the collection device in mls/minute

t is the time over which the sample was collected in minutes

If the half-life of the radionuclide is short enough that significant decay occurs during the sampling time, a more elaborate equation is used to calculate C. If significant decay can occur between the end of sampling and the start of the count, that would be corrected for by using the standard decay equation. There seems to be a mistake in your equation 1: Average concentration x average stack flow rate divided by correction factor would give a release rate (Q) in curies per unit time (for example, Ci/min) not an activity in curies: Ci/liter x liters/minute = Ci/min Equation 2 seems to be calculating the total activity released during a defined period, for example, a controlled release, because it refers to the duration of the release. I would not describe this as periodic sampling but that is just semantics. All that is going on in this equation is that the release rate (Q in my equations) is multiplied by the duration of the release in order to calculate the released activity. However, the meaning of "post-lab correction factor" and "sampler operation efficiency factor" elude me. Presumably they have a simple explanation and are described in the literature you have. Paul Frame, CHP, PhD