When nuclear materials are handled it is important to be sure that none goes missing. The materials are protected at all times and levels of security at nuclear sites are very high. These levels of security are based on national and international guidelines.
Detailed records are kept of all nuclear materials that are received and processed at nuclear sites. International authorities regularly monitor how civil nuclear materials are handled and accounted for. This is to confirm that no nuclear material is missing or used for unauthorised purposes. The monitoring involves a series of checks and inspections carried out by multinational teams of inspectors.
These checks provide an overview of the systems that keep track of civil nuclear material and the records of the quantities involved. Material Unaccounted For (MUF, also known as Inventory Difference) is part of the terminology used in nuclear materials accountancy and safeguards as one indicator of the quality of control of nuclear materials. It works in a manner analogous to financial book-keeping. At the start of an accountancy period, the books are in agreement with the stock or inventory. As new items are brought on to the inventory the book account is increased, and for items leaving the inventory it is decreased. At the end of the accountancy period, the stock is compared with the book account. This is no different in principle to what is done in shops, banks, warehouses and factories.
MUF = (Physical Inventory) - (Book Inventory)
Where...
Book Inventory = (Opening Inventory) + (Receipts) - (Issues)
A positive value of MUF means there is more material than recorded in the book (i.e. an apparent gain), while a negative value suggests an apparent loss.
MUF can arise from a number of factors:
In situations where the items remain unchanged during the inventory period, MUF is expected to be exactly zero. A nuclear reactor is such a case (if, for accounting simplicity, no distinction is made between fresh and irradiated elements). Fresh fuel elements are received at the reactor and added to the inventory; irradiated elements may be transferred to an off-site storage pond to cool or to a reprocessing plant, at which time they are subtracted from the inventory. The extremely rare occasions when a non-zero MUF occurs will virtually always be because of a book-keeping error. For example, an item was not recorded as having entered or left the reactor site. A check of the receipts and dispatches paperwork would usually identify the mistake, which can then be rectified.
The situation is different in a plant where the material undergoes a process that changes its nature. Not all the material that goes into processing plants comes out as finished product. An example is a reprocessing plant, where irradiated fuel enters, is dissolved, and passed through a chemical separation process to extract potentially re-usable nuclear material remaining in the fuel. Besides the product emerging from the plant, various waste streams also have to be taken into account, including the small amounts of nuclear material released into the environment under the independently monitored and controlled discharge authorisation. MUF is calculated using the equation above. In simple terms, the output is compared with the input to see if they balance (note that in modern such facilities, a system known as near real time material accountancy (NRTMA) is also used to provide frequent updates of nuclear material balances, including estimates of in-process inventories).
In order to help minimise MUF, physical inventories for these plants are undertaken when the nuclear material in them is consolidated into forms and at locations where the most accurate measurement techniques can be applied. For example, measurements of waste and residues, which are often heterogeneous and therefore generally require non-destructive assay (NDA) techniques, tend to have much larger uncertainties than liquor in tanks. It is therefore important to limit amounts of waste and residues, to facilitate accurate accountancy.
After the fuel has been dissolved, it is usually put into a special tank where an accurate measurement of the nuclear material content can be made. The amount of nuclear material cannot be measured with absolute accuracy, however; there is an uncertainty associated with every measurement, be it the volume of liquor, its density or the concentration of nuclear material. If such parameters are measured several times, slightly different answers will generally be obtained each time. At the dissolution stage, some of the fuel may turn out to be insoluble, leaving some material in solid form. This will normally be declared as waste, but it has to be measured and the techniques used have a relatively high uncertainty compared with those for the dissolved liquor. At this point, the total amount of nuclear material entering the plant has been measured, but unlike the reactor example discussed above where items are simply counted and the number known with zero uncertainty, there is an uncertainty on the amount. So if, say, 100 kg of nuclear material is present, it could be measured as 100.8 kg or 99.5 kg or any amount close to 100 kg.
The same principles apply to the material coming out of the plant. Knowledge of the amount of nuclear material product will have a small uncertainty within a range determined by the accuracy of the measurement techniques. Again, the material emerging in waste streams will be subject to a relatively larger uncertainty than the product material.
When the various figures are inserted into the MUF equation described above, the two sides will not give a zero MUF (except on very rare occasions) because the components of the equation cannot be determined exactly. So, even if none of the effects other than measurement uncertainty listed above are present, the MUF will be non-zero. In theory, the MUF arising from measurement uncertainties should be as often positive as negative over a long period, but some measurement techniques may overestimate or underestimate the quantity (i.e. they are biased), giving rise to MUFs frequently of the same sign.
If the MUF appears to be abnormal, an analysis is carried out to see if the MUF is consistent with the measurement uncertainties. If it is much larger than those uncertainties imply, then the anomaly will be investigated more thoroughly. For example, any unmeasured inventory on the output side of the plant will bias the MUF towards negative values. Some material will inevitably remain inside a plant (so-called hold-up), even after a washout (e.g. in nooks and crannies, or plated out on the walls) but such amounts are normally small. However, there is a possibility that material could get into places where it is not expected. For example, spills of liquor may leave material which may only be recovered when the building is decommissioned. Unmeasured discharges to the environment should, if they exist at all, be extremely small, but would generally put a negative bias on the MUF if they were present.
In operations today, unmeasured material should be very small, as all known streams in plants are measured. This was not always the case in the past. Thirty or more years ago, the technology to measure some waste streams, for example high active and intermediate-level solid waste, was not available. Material leaving the plant by such routes was therefore then included in the MUF.
In addition to nuclear materials accountancy, there are a number of other controls employed to detect the unauthorised removal, including theft, of small amounts of nuclear material. In common with other industries, these controls are based primarily upon security and include:
To gain sufficient assurance of the non-diversion of nuclear materials, the international safeguards inspectorates supplement their verification of nuclear materials accountancy by techniques such as design information verification (to confirm that plant design and operation remains as declared) and the use of containment and surveillance (e.g. sealing devices and cameras).
In summary, even if all of the nuclear material entering a plant emerges in streams that are measured, a non-zero MUF is unavoidable due to measurement uncertainties. Only in item counting situations is MUF expected to be exactly zero. The fact that there is a MUF does not necessarily mean that there has been a gain or loss of nuclear material.