Dose Rate from a Radioactive Volume Source Calculator

Please read the user notes below the calculator to make best use of its features. 

Release notes

[Ionactive comment: All our in-house radiation protection calculators are designed to be simple to use and self explanatory. With our volume source calculator we do encourage the reader to carefully read the following notes and examine the source geometry diagrams to make best use of this resource. 3d calculations are on another level and the code under the hood is significantly more sophisticated when compared to the point, line and planar Ionactive resource. For this reason we have restricted the capability of this V1 release whilst we obtain user feedback. This feedback will be considered for our V2 release which we are working on right now.]

Version 1.0  The Dose Rate from a Radioactive Volume Source Calculator has two operational modes:

• Forward (Activity / Concentration  → Dose Rate): This mode allows you to calculate the dose rate from a volume source at a total activity (of a volume you specify), or as an activity per unit volume (e.g. Bq/m³).
• Reverse (Dose rate  → Activity / Concentration): Here you may enter known, measured or assumed dose rate data and infer the potential activity of the volume source (assuming uniform activity per unit volume). 

The parameters, choices and inputs will vary slightly between the two modes selected. In almost all cases, if you make a change to the variables then you need to click calculate to see the changes. 

We first consider input choices for the forward calculation. 

• Calculation Mode: Here you select Activity / Concentration  → Dose Rate (forward) or Dose rate  → Activity / Concentration (reverse).
• Radionuclide: Select from a popular list of beta / gamma radionuclides covering medicine, industry and of historical significance.  
• Unit system: Choose SI or Non Si units (you cannot mix between the two).
• Output format: Choose normal or scientific.
• Dose quantity: Select either effective dose rate, or absorbed dose rate in air.
• Geometry: You can select either a box (where you later specify dimensions in the X,Y and Z plane) or a cylinder (where you later specify the radius and cylinder height).
• Source input mode (forward): The default choice is Total activity, but you can alternatively choose activity per unit volume (e.g. Bq/m³ etc).
• Source medium: Here you select what the source volume consists of (choices in V1 release are air, water or concrete of various densities).
• External shielding: choose to add either lead, steel, concrete (several densities given) and water. If this setting is used then the shielding thickness input fields will appear where the thickness and desired units can be entered.
• Total activity or activity concentration (depending on source input mode selection): Enter total activity or activity concentration of the volume source.
• Volume source dimensions: For the box source enter the X,Y and Z dimensions, for the cylinder enter the radius and height (selectable units for both).
• Detector distance from source surface: Enter the detector distance (calculation point) using selectable units from the source surface. For this V1 release the following diagram will explain the geometry and current limitations. 

In the above diagram X, Y and Z are specified dimensions for the box source, and R (radius) are H are specified dimensions for the cylinder source. C is the calculation point with indicated orientation. Future versions of this calculator will allow allow offsets to place C anywhere around the selected volume source. 

• Dose scaling output: Choose base for Gy / Sv / R etc, or micro, milli, kilo etc as desired. 

At the bottom of the calculator is the calculate and reset buttons. Use the calculate button each time you make a change to the desired inputs. The reset button will revert the calculator to standard settings as if the page has been reloaded. 

The outputs in the Forward (Activity / Concentration  → Dose Rate) direction are as follows.

• A summary of the calculation case. Note that this will include two dimensions, the distance between calculation point and the surface, and also between the calculation point and centre of the volume source (where the calculation reference point is located).
• Finite volume dose rate (in effective dose rate or absorbed dose rate in air)
• Point source dose rate (if located at surface)
• Point source dose rate (as if located at the centre of the volume).
• Volume / point ratio (based on surface of the volume)
• Volume / point ratio (based on the centre of the volume). These ratios are useful  for investigating how the inverse square law may apply, and if volume source calculations are actually needed. For example try a small cube (mm sides) and a distance of 1m and note the ratio results.
• Total activity used in the calculation.
• The calculated volume of the source.
• The activity concentration used (e.g. activity per unit volume).
• External shield status (none by default).  If shielding is selected then the shielding parameters will be shown here in the form of material, thickness and transmission (T). 

Important note on the point-source comparison results. The two point source comparison results (“point source at the same stand-off distance” and “centre-equivalent point source”) are intended only as idealised reference cases. Since these comparisons are treated as point sources with negligible size, they are calculated without any source medium self-shielding, even if a source medium such as water or concrete has been selected for the finite volume source. This means that changing the source medium affects the finite volume source result (as expected), but does not affect the point source comparison results, unless optional external shielding has also been applied, in which case that shielding is applied to all results. In other words, the point source comparisons are included to show the effect of source geometry and distributed activity, not to represent a true point source physically embedded within a bulk medium. A true point source burried within a volume is another calculator for another day!

We now consider the input choices for reverse calculation (Dose rate  → Activity / Concentration). Only those different from the forward calculation will be featured below. 

• Target dose rate: This is the dose rate that has been measured or is required, and which you wish to use in the calculation of volume source activity. You can enter dose rate with appropriate input scaling factor, and choose to output as inferred total activity or an activity concentration.  

The outputs in the reverse calculation are as follows:

• A summary of the calculation case.
• Required activity (for given dose rate) e.g.  Bq (depending on input settings)
• Required activity concentration e.g. Bq/m³ (depending on input settings)
• Point source and centre-specific point source dose rates (comparative dose rates IF a single point source is assumed at the face of the volume source, or at its centre)
• Shielding data, if selected for use in the calculation. 

The advantage of looking at the point source data is to determine how far you would be from the 'true' dose rate (or activity) if you were to assume a point source rather than a volume source. 

Have a play with the calculator and see what results you can come up with in both forward and reverse mode. 

Some example uses

Here we will describe a few example uses of this volume calculator.

I-131 delay tank in a hospital

A hospital has an I-131 delay tank in the basement. It is used to collect radioactive aqueous waste from the nuclear medicine department, specifically the 'hot WC', 'hot disposal sink' and 'hot shower'. The radioactive waste is held (delayed) in the tank for a week or two before discharge to the sewer network is permitted. The tank dimensions are X=4m, Y=3m and Z=3m. The tank is made of steel with a wall thickness of at least 2mm. If the tank was nearly full, and contained 4 GBq of I-131, what would the dose rate be at 1m from the tank (facing the Y/Z face of the tank). This example is depicted in the diagram below. 

Using the Ionactive calculator with the above parameters we see the following output:

5.22 µSv/h effective dose at 1m. 

Note that the volume / point ratios are low (e.g. same stand-off value is 0.02589)  - this indicates that a point source comparison calculation is a poor substitute for a specific volume calculation (which should be quite obvious given the geometry). 

If the above result is compared to MicroShield we see 4.86 µSv/h effective dose at 1m (using the ICRP 116 dose conversion coefficients). We think pretty good given our much simpler model! Remember that point source calculations are easy, and mostly likely comparable over many calculators. Volume source calculations are much more difficult, so reasonable agreement with industry standard professional software is a win win. 

Given that 2mm of steel for I-131 is not likely to make a huge different we note that if the steel is removed from the calculation then the Ionactive calculator outputs  5.67 µSv/h as compared to the MicroShield output of 5.184 µSv/h.  This is pretty good agreement for our freely available calculator. 

Small volume source comparison to a point source

Consider a 1GBq  Cs-137 volume source of 2cm, by 2cm, by 2cm (source medium is air for simplification). What is the effective dose rate at 1 m from this source?

Plugging the values into the calculator will show that the dose rate is 76.23 μSv/h at 1m. Now look at the volume / point ratio for same stand-off and centre-equivalent stand-off point. The values are 0.98 and 1.00 respectively. This shows, as expected, that in this particular case a point source treatment of this scenario is as good as a more complicated volume treatment.