Corresponding author: Olga V. Shmidt (

Academic editor: Yury Korovin

There exist different variants of organizing the closure of nuclear fuel cycle (

Incorporating fast neutron reactors into the nuclear power structure needs to be accompanied by the introduction of a closed fuel cycle, that is, a system for irradiated nuclear fuel processing and “fresh” fuel production using recycled nuclear materials (

As part of the

Until recently, mathematical simulation of the

As a tool for justifying the engineering and design solutions to be used by process engineers, equipment developers and designers of out-of-pile NFC process stages, a code, VIZART (

calculation of the material balance, including depending on time, and taking into account the evolution of the material flow nuclide compositions;

simulation of individual processes and devices for justifying and optimizing process conditions;

calculation of key indicators for processes and devices taking into account the performance of equipment and different process conditions.

Integrated processes, such as

VIZART simulated entities.

A process (process operation) is the base simulated entity. Its key functional purpose is to convert the incoming flow to an outgoing flow based on dedicated algorithms that implement the mathematical model of the process. Characteristics of the process, such as chemical reactions or dependences of the product properties on the process running conditions, are used to calculate the conversion. Each process node is a component of the flow diagram used to describe physical objects (devices, plants, etc.) in simulation problems. The key characteristic of a process node is the set of processes (consecutive or parallel) occurring on the process node. Apart from processes, a process node is characterized by a set of equipment (device, plant,…) properties, efficiency, maximum incoming flow rate (mass flow rate, volume flow rate, loading frequency and volume), as well as by the lifecycle characteristics: operating time, frequency of preventive maintenance, etc. A processed product (flow) is a combination of chemical substances (materials) entering or exiting the process node or the process.

Due to the absence of final

Calculations can be done both in the steady-state mode and in the dynamic mode for one and the same flow diagram, this being supported by the VIZART object-oriented approach tools.

Fig.

General view of the VIZART user interface (Russian version).

The VIZART code allows several types of simulation for the CNFS process stages, including steady-state and dynamic mode calculation of the material balance, and optimization of the characteristics of processes a processing line includes.

Calculation results are displayed as tables (Fig.

Material flow characteristics (Russian version).

Automation of the material balance calculation reduces the number of routine hand computations, and cuts the number of errors and the time for preparing initial data. The dynamic environment for the computational pattern preparation and the possiblity for changing the user interfrace parameters make it possible to consider a large number of diffent options for process solutions, and, accordingly, select the most appropriate alternate flow digharam.

solutions for configurations of processing lines taking into account the existing requirements for efficiency, operating consistency of process stages, and generation dynamics for intermediate and end products;

accumulation of fissionable and nuclear materials at different process stages, and in intermediate storages and tanks, which is initial information for assessing safety and compliance with nonproliferation criteria;

volumes and types of generated RW.

The initial information specified for each flow diagram node in the course of dynamic calculations includes duration of the operation, loading frequency and volume, consumption rates of material flows, and capacity of devices. Based on the calculation result, the cyclogram of the equipment operation is plotted (Fig.

Example of the equipment operation cyclogram calculated in the VIZART code (Russian version).

We shall consider the possibility of selecting the parameters of process operations based on the example of a combined pyrohydrometallurgical flow diagram for reprocessing mixed nitride uranium-plutonium (

Overall view of a combined

It was shown based on the calculation results that the expected daily electrolytic cell loading of 8 kg of

The

optimizing the processing line configuration using a set of process nodes and operations;

optimizing the processing line configuration in terms of efficiency and the material flow processing time;

optimizing process modes and operations to comply with the

As a rule, the replacement of nodes and operations leads to a major change to the entire process chain or, at least, to the nodes associated with them. Automation of such changes is hard to implement. In this case, one can speak about optimization only in terms of comparing a number of the layout options based on the preset integral characteristics of the flow diagram as the whole, and the notion of global optimum becomes indefinite. Therefore, optimization, as understood in the classical mathematical theory, can be spoken about only in the event that the set of process nodes is defined and fixed. Therefore, no flow diagram is expected to be varied in the course of optimization.

A classical optimization problem is formulated as follows:

where

The structure of set

The solution of the optimization problem is traditionally broken down into three stages:

construction of the processing line (process) model;

statement of the optimization problem, that is, definition of the target function, variable parameters, and the set of constraints;

solution of the optimization problem using the selected method.

The process model is built using the VIZART user interface. To solve the extremum problem, a dedicated subsystem has been developed, which includes window interface forms for setting the optimization parameters, and modules which allow one to search for the target function extremum and to compute the target function values based on the results of calculating the flow diagram characteristics. Variable optimization parameters are process modes and the efficiency and loading characteristics of equipment.

The following integral characteristics calculated in the course of the simulation are used as optimization criteria:

deviation of concentrations of chemical elements in end and intermediate products from preset values;

efficiency of the processing line;

deviation of the physicochemical characteristics of intermediate and end products from target values to be transferred to further operations and stages (density, particle size, flow temperature, flow composition).

Refabrication cost of 1 kg of nuclear fuel (with capital costs taken or not taken into account) can be used as the versatile criterion for the entire package of the

One of the most frequently solved problems in optimizing processing lines of radiochemical production facilities is harmonization of efficiencies for different operations production departments or the entire flow diagram include. Thus, optimization was demonstrated in

In connection with the complexity of the simulated system, it is not possible to formulate assumptions with respect to the target function topology and the global extremum location, including the target function continuity and smoothness. No gradient methods, which require computation of derivatives, can be used therefore for the extremum problem solution. Among non-gradient methods, the modified deformed polygon method has proved to perform well (in Nelder, Mead 1965). The major issue in employing this method is its convergence to the local minimum that depends on the selected initial approximation. A combined algorithm has been therefore developed when a set of initial approximations is selected at the initial stage using a genetic algorithm (in Different Evolution: genetic algorithm for functional optimization), for each of which the optimal value of the target function is determined. The global minimum is determined based on the obtained target function values.

Considered as the test problem for demonstrating the operation of the proposed algorithm was the problem of optimizing based on the VIZART code the characteristics of the fuel fabrication flow diagram fragment comprising the following operations: disintegration of uranium and plutonium nitrides, granulation of powders, mixing of powders with zinc stearate, compaction of fresh pellets (Fig.

A fragment of the fuel fabrication flow diagram.

The problem consisted in minimizing the time for the fresh pellet production from the preset number of mixed nitrides.

The parameter “compaction time” was varied at stage 1. The overall process duration depends linearly on the durations of process operations, and, therefore, a trivial task was considered. As an answer, the optimization process produced the optimal value at the lower range boundary, having confirmed so that all components of the optimization subsystem operate correctly.

The parameter “nitride disintegration time” was varied at stage 2. For the preset parameters of the powder granule disintegration time and size limits, equal to 60 min and 10 μm respectively, the dependence of the granule size on the initial size and time changes according to the law shown in Fig.

Powder granule size as a function of time and initial size.

Total process duration as a function of initial size and disintegration time.

As a result of the optimization, the nitride disintegration time (33.2 min) was found which ensured the smallest possible process duration of 69 h 23 min.

The VIZART code makes it possible to solve a broad range of problems involved in development, justification and optimization of the

Application of mathematical optimization methods makes it possible to update the characteristics of processes based on integral criteria. Target functions need to be described for these to be used more efficiently.

At present, the VIZART code addresses primarily prediction problems due to which it does not require certification. To confirm the adequacy of the VIZART-based calculation results, tests are conducted to find out if the calculations used in the code algorithm coincide with the calculations obtained by an alternative method or with the results of operating real production facilities. The code will require to be certified in the event of the calculation results used in justifying safety of processing facilities.

Russian text published: Izvestiya vuzov. Yadernaya Energetika (ISSN 0204-3327), 2023, n. 4, pp. 5–18.