Answer to Question #11193 Submitted to "Ask the Experts"

I'm working on an optimization analysis of a radiological fume hood. I've searched the literature and have not yet found information I need.

I am looking for how to calculate the contamination of air in a radiological fume hood from liquid radioactive samples in the fume hood. The samples are ²³⁹Pu, ²³⁸U, ¹³⁷Cs, ²⁴¹Am, and ⁹⁰Sr.

Also, I need to calculate the amount of radioactive deposition/plating on the hood's ducting from the liquid samples.

Is there a free-source computer model I can use?

Any references, equations, and explanations on the approach to this problem would be much appreciated.

I would expect that none of the radionuclides that you cite would be volatile from liquid solutions by evaporative processes. The only way they would become airborne would be through physical agitation of the solution—e.g., boiling (generating airborne droplets), stirring, transferring liquids to or from the containers, etc. The cesium could volatilize if the temperature were sufficiently high, but such temperatures would not apply in the case of typical liquid solutions.

In such cases it is generally not possible to predict what the expected air concentrations of radionuclides might be in the hood air/exhaust. Such concentrations are normally determined by measurements in which an air filter holder with a high-efficiency filter is placed in the exhaust duct of the hood (or in the hood itself if you want to know the in-hood concentration). Using an air pump connected to the filter holder with tubing, air is drawn through the filter at a constant rate for a known time; the filter is then removed and analyzed using appropriate counting equipment to determine activity concentration(s), based on the counting results, conversion to activity, and the known volume of air sampled. It is possible to do a study in which variables that affect production of airborne contaminants are each varied individually while collecting a respective air filter sample. In some cases it is then possible to fit the production rate with the variables in a useful mathematical model.

In the rare instance when you might already know how rapidly a particular radionuclide is being released into the hood, you could make an estimate of the expected air concentration in the exhaust air. If P is the release rate into the hood (e.g., Bq s^-1) and F is the volumetric flow rate of the hood (e.g., m³ s^-1), the quotient of the release rate by the flow rate, P/F, would provide an estimate of the activity concentration in the exhaust air from the hood, assuming that the activity mixed uniformly with the exhaust air.

Regarding deposition of radioactivity on the hood ducts, this is often very difficult to predict because such processes depend strongly on many variables, including such things as particle size distributions associated with the radioactivity, size and geometry of the ducts, smoothness of the duct walls, and other materials already deposited on the duct walls, length of the ducts, bends or transitions in the ducts, air flow characteristics, etc. The most direct and reliable approach is often to attempt to make measurements of deposited activity by taking wipes of the duct walls. This may be difficult and in some cases impossible, but some facilities do have access locations. If it can be done it is likely that you could fit the results to a mathematical model that would adequately predict depositions for the same operating conditions. (If there is potential for release to the outside air of any significant amounts of some of these radionuclides, such as the plutonium and americium, the hood may be equipped with an air filtration cleanup system containing large absolute filters that filter all the air leaving the hood and that are designed to retain practically all of the airborne particulates incident on the filter.)

If your situation involves turbulent flow within the duct (often associated with bends in the duct, duct size transitions, and/or high air velocities in the duct), theoretical modeling is often extremely difficult and sometimes impossible. For full turbulent flow (not likely the case for hood ducts) some predictive theoretical and/or semiempirical modeling has been done—see, for example, a paper by Sippola and Nazaroff and a second paper by the same authors. In some instances people have resorted to development of appropriate models based on experimental measurements, as referred to in the previous paragraph. There have been numerous papers written regarding particle deposition in ducts. Some of these have attempted to perform modeling of the deposition process. You can easily find many references to these by searching the Internet for “particle deposition in ducts” and related topics. There are also references to models and codes that have been written and used, although their availability may be questionable. A number of these have involved Monte Carlo simulation type approaches. I would recommend that you also refer to some commonly employed references such as ISO 2889:2010 and US Nuclear Regulatory Commission NUREG-1400 that may have some useful information. A couple of other references that discuss particle loss through sampling lines may be helpful in describing some of the approaches taken to describe losses of small particles, primarily by diffusion, as air is transported through confining tubes; here are links to an available paper by Kumar et al. and another by Von der Weiden et al. describing software for a particle loss calculator.

Good luck in your attempts to develop adequate models for the particle deposition.

George Chabot, PhD, CHP