On monitoring and forecasting of graphite stack temperature in transient modes

The paper presents a method of monitoring and forecasting of the graphite stack temperature of the RBMK reactor in transient modes. The method is based on processing the in-core information about macro-distribution and mathematical model of distribution of temperature changes of the graphite stack in the reactor core. It is shown that the use of archival neutron field monitoring data allows determining the graphite stack temperature in the on-line mode.


Introduction
One of the requirements for the control process of the RBMK reactors is the effective and safe operation of the reactor under changes in power level [1][2][3]. In this regard, the task of monitoring and forecasting of changes of the operational reserve in space and time is relevant, as the operational reactivity margin determines the reactor maneuverability (the operational reactivity margin below refers to the value , i.e. the excess of birth rate over one). The change of the propagation coefficient in the RBMK reactors due to the influence of feedback can be represented as follows [3,4]: is the change of the propagation coefficient due to the following reactivity effects: steam, fuel and moderator temperature, and xenon concentration, respectively.
In this article the problem of the forecasting of the propagation coefficient changes under the moderator temperature changes is considered. It is assumed that the following relationship is true: is the graphite reactivity coefficient (a known function). Thus, under the assumption made above, the task of monitoring and forecasting of the reactivity changes is reduced to the problem of monitoring and forecasting of the graphite temperature changes in transient modes of the reactor.

Mathematical model
To describe the behavior of macro-distribution of the graphite temperature changes in the RBMK reactor core we use the following mathematical model, which is applied in the study of RBMK reactors dynamic characteristics [5][6][7]: is deviation of neutron flux distribution at time  from the initial value. The model (3) does not account for the leakages of heat over the height and radius of the reactor. Let us present the equation (3) in a dimensionless form. To do this, we introduce a new variable where S С T T  is the average temperature difference in the reactor in the steady state at nominal power level.
where S T is the water saturation temperature under the working pressure in the channel.
Then the original problem (3) can be written as:

Solution
The solution of the problem (5) presents no difficulties on condition that the values С  and However, with a real RBMK reactor the problem of definition of macro-distribution of the graphite temperature using the model (5) is complicated by the following circumstances: 1) the parameter С  may be a function of coordinates and significantly depend on the operating conditions, in particular, the composition of the gas mixture of the graphite stack [3,5,9]; 2) the experimental information on the energy release distribution in the reactor core is available only in a finite number of coordinates (at the locations of sensors) and is presented in the form of currents of sensors at discrete moments of time; 3) the impact of a large number of perturbing factors leads to the fact that the distribution of energy release under the reactor power change may differ from the forecast. Strictly speaking, this difference is random and from a mathematical point of view is described with a random function. Regarding the first comment let us assume that the time constant of the graphite С  does not depend on the coordinate and can be determined experimentally. The rest of the comments can be considered as follows.
Deviations of currents of discretely located sensors of energy release from the initial values are approximated with a set of test functions according to the methodology [8,10]. This approach to determination of the graphite temperature macro-distribution can be justified by the fact, proven by the archival experimental information, that the distribution of the graphite temperature changes is a fairly smooth function. The The interval between the time counts is considered to be constant: . Then the expression for the macro-distribution of the graphite temperature changes is as follows: With this in mind, the forecast for the change of graphite temperature in the reactor core can be carried out according to the formula: ,

On accuracy of monitoring macro-distribution of the graphite stack temperature
To evaluate errors in graphite temperature macro-distribution let us assume the following [8]: In this case it is possible to show that the error of monitoring the behavior of macro-distribution of graphite stack temperature under the steady mode of measurements is determined by the period of getting the sensors readings 0  , by the parameters of the neutron flux correlation function and variance of the error of restoration of neutron flux space distribution, and does not exceed 4% in stable mode.

Conclusions
The methodology of monitoring and forecasting of the graphite temperature changes in the RBMK reactor core is proposed.
The methodology is based on using both experimental information (current of sensors and thermocouples in the graphite stack) and the mathematical model of the distribution of the graphite temperature changes in the reactor core. The mathematical model is obtained considering the number of assumptions, namely: the reactor height and radius heat leaks are not considered, the graphite time constant is considered to be constant within the reactor core. The algorithms for the monitoring and forecasting of the graphite stack temperature changes in the reactor core are easy for computer implementation and require small amount of RAM. Estimation of the errors of the graphite stack temperature forecasting and monitoring allows us to conclude that the proposed algorithms can be used to forecast and monitor with a reasonable degree of accuracy.