Packing optimization problems have a wide spectrum of real-word applications. One of the applications of the problems is problem of placement of containers with spent nuclear fuel (SNF) on the storage platform. The solution of the problem can be reduced to the solution of the problem of finding the optimal placement of a given set of congruent circles into a multiconnected domain taking into account technological restrictions. A mathematical model of the prob-lem is constructed and its peculiarities are considered. Our approach is based on the mathematical modelling of rela-tions between geometric objects by means of phi-function technique. That allowed us to reduce the problem solving to nonlinear programming. Today, an important scientific problem is the problem of creating conditions for safe storage of spent nuclear fuel. In the process of creating any dry spent nuclear fuel storage, the following main stages can be identified: site selection, storage design, construction, operation and decommissioning. A full check for compliance of the repository and its elements with these standards usually begins at the design stage. At the stage of site selection, the inspection for compliance with safety standards is carried out only in terms of the impact of the repository as a whole on the environment. This approach cannot be considered fully appropriate, because, taking into account, for example, all the climatic features of the future storage site, it is possible to adjust the thermal storage regimes of spent nuclear fuel. Similarly, it can be considered necessary to analyze and select the shape of the storage site in order to accommo-date the maximum possible number of spent fuel containers. Such a choice, obviously, should be made taking into ac-count the norms of nuclear, radiation and thermal safety, as well as in compliance with technological limitations. The problem of finding the optimal placement of containers taking into account the given technological limitations can be formulated in the form of the problem of optimization of geometric design. Therefore, the purpose of the study is to build a mathematical model of the problem and study its characteristics to develop effective methods of solution. The proposed approach is based on mathematical modeling of relations between geometric objects using the method of phi-functions. This allowed to reduce the solution of the problem to the problem of nonlinear programming.
MODIFICATION OF MATHEMATICAL MODEL OF EVAPORATOR FOR SPENT NUCLEAR FUEL RADIOCHEMICAL REFINING