Point kinetics model

A simplified transient analysis model of the sulphur iodine and Westinghouse hybrid sulphur cycle was presented by Brown, et al. (2009). This model is utilised in this paper via coupling to a PBMR-268 model and a simple point kinetics model. Some of the key tenants of the analysis model are summarised however interested readers are referred to the original paper for greater detail. The S-I and HyS analysis model is a control-volume model which treats the chemical plant as a closed system. 

The nuclear reactor kinetics was modelled using simple point kinetics. The point kinetics model utilised in the calculation was developed as an analogue to the point kinetics module of the RELAP5 code. The number of delayed neutron groups considered was six. A Doppler feedback coefficient of -0.0095 was used. Xenon feedback was also modelled, although due to the time scales considered in this document the xenon feedback is not relevant and has almost no impact on the results. 

First, a steady-state solution is attained in both the THERMIX model and hydrogen model. Second, a transient is initiated, either in the chemical plant model or in the point kinetics model. Finally, the THERMIX, point kinetics and hydrogen generation models all interact in each time step. The integration scheme is shown in Figure 4. 

Coupling of the codes is performed through the IHX. The data exchanged between the codes consists of the flow rate and temperature of helium through both hot and cold legs of the IHX. The hydrogen model calls THERMIX and the point kinetics model every time step and then new temperature and flow rate values are returned. This process is repeated each time step. 

A transient control volume model of the S-I and HyS cycle is presented. An important conclusion based on the results of this model is that the rate-limiting step of the entire S-I cycle is the HI decomposition section. In the HyS cycle, the rate-limiting step is the H2S04 decomposition. A generalised methodology for coupling these thermochemical cycle models to a nuclear reactor model is overviewed. The models were coupled to a THERMIX-DIREKT thermal model of a PBMR-268 and a point kinetics model. Key assumptions in the PBMR-268 model include flattening of the core and parallelisation of the flow channels. 

Considering the fact that the MCC is divided into two symmetric loops, a pipe break in one of these directly affects the thermohydraulic and neutronic behaviour on one side of the core. The resulting asymmetry in reactivity and power has to be assessed by a 3-D code. OptionaUy, the information obtained can be compiled as input for use by a point kinetic model, which, however, usually requires some iterations. 

In a conventional point kinetics model, involving the concentration of xenon and the flux tending to bum it out, the problem is nonlinear. However, it seems reasonable to make the prompt jump approximation in which the neutron lifetime and the lifetime of the precursors are neglected in comparison with the periods of the iodine and xenon isotopes governing the problem. We can then regard the flux as a control variable that can be adjusted to different levels as required in an optimum program. 

There is an obvious generalization to time-dependent theory 10) which may have some part to play in reactor kinetics and stability problems, even at the point kinetics model level. Although the formal expressions are easily stated, the utility of this nonlinear theory has yet to be demonstrated. 

The SSC-K code [4] has been developed by KAERI for the analysis of system behaviour during transients. The SSC-K code features a multiple-channel core representation coupled with a point kinetics model with reactivity feedback. It provides a detailed, one-dimensional thermal-hydraulic simulation of the primary and secondary sodium coolant circuits, as well as the balance-of-plant steam/water circuit. 

The plant transient analysis code for the Super FR is called SPRAT-F. It is based on the 1-D node junction model with radial heat transfer and point kinetics models such as SPRAT-DOWN for the Super LWR (see Chaps. 4 and 6). The nodalization is shown in Fig. 7.67. The models used in SPRAT-F are the same as those in SPRAT-DOWN. The turbine control valve regulates the main steam pressure by changing the main steam flow rate as in BWRs and the Super LWR. The relation between its stroke and the steam flow rate is the same as that of the Super LWR (Fig. 4.4). The relation between the core pressure and the feedwater flow rate (with constant pump speed) is also the same as that in the Super LWR (Fig. 4.5). 

The RELAP5-3D model simulates the fast gas reactor with a point kinetics model using separable feedback terms and standard fission product decay based on the 1979 American Nuclear Society standard for Separable feedback maintains the kinetics feedback due to fuel, moderator, and structure temperatures separately. 

For simplicity of calculations, most of the large system codes consider the point kinetics model assuming the overall buckling to be almost constant during the transient. The parameters used in these equations such as delayed neutron fraction, prompt neutron life time, delayed neutron precursor concentration, etc. are defined taking into account some phenomena formally neglected during the derivation of the point kinetics equation. An improvement to the... 

The simplest model of time-dependent behavior of a neutron population in a reactor consists of the point kinetics differential equations, where the space-dependence of neutrons is disregarded. The safety of reactors is greatly enhanced inherently by the existence of delayed neutrons, which come from radioactive decay rather than fission. The differential equations for the neutron population, n, and delayed neutron emitters, are... 

A feed concentration of 15 g glucose and 15 g xylose per litre was used over a feed rate of 20-200 ml/hr. Samples were taken at successive points along the reactor length, and the usual analysis for glucose and xylose consumption, organic acid production and cell density were done. A kinetic model for the growth and fermentation of P. acidipropionici was obtained from these data. 

The development of methods for the kinetic measurement of heterogeneous catalytic reactions has enabled workers to obtain rate data of a great number of reactions [for a review, see (1, )]. The use of a statistical treatment of kinetic data and of computers [cf. (3-7) ] renders it possible to estimate objectively the suitability of kinetic models as well as to determine relatively accurate values of the constants of rate equations. Nevertheless, even these improvements allow the interpretation of kinetic results from the point of view of reaction mechanisms only within certain limits ... 

FIGURE 4.23 In the kinetic model of gases, the molecules are regarded as infinitesimal points that travel in straight lines until they undergo instantaneous collisions. 

The kinetic models are the same until the final stage of the solution of the reactor balance equations, so the description of the mathematics is combined until that point of departure. The models provide for the continuous or intermittent addition of monomer to the reactor as a liquid at the reactor temperature. 

This section is divided into three parts. The first is a comparison between the experimental data reported by Wisseroth (].)for semibatch polymerization and the calculations of the kinetic model GASPP. The comparisons are largely graphical, with data shown as point symbols and model calculations as solid curves. The second part is a comparison between some semibatch reactor results and the calculations of the continuous model C0NGAS. Finally, the third part discusses the effects of certain important process variables on catalyst yields and production rates, based on the models. 

Let s discuss the reaction rate computations based on the kinetic model with those derived from the experiments. At a given instant, these calculations are essentially "point" functions since they are independent of the path the reaction system has taken up to that given instant. 

The failure to identify the necessary authigenic silicate phases in sufficient quantities in marine sediments has led oceanographers to consider different approaches. The current models for seawater composition emphasize the dominant role played by the balance between the various inputs and outputs from the ocean. Mass balance calculations have become more important than solubility relationships in explaining oceanic chemistry. The difference between the equilibrium and mass balance points of view is not just a matter of mathematical and chemical formalism. In the equilibrium case, one would expect a very constant composition of the ocean and its sediments over geological time. In the other case, historical variations in the rates of input and removal should be reflected by changes in ocean composition and may be preserved in the sedimentary record. Models that emphasize the role of kinetic and material balance considerations are called kinetic models of seawater. This reasoning was pulled together by Broecker (1971) in a paper called "A kinetic model for the chemical composition of sea water."... 

Fig. 13 Amount of polymer as measured by the IR absorption at 2852 cm with respect to time. The kinetics observed on a rough catalyst is represented by crosses. The line through these points is a fit to the kinetic model given in the text. Kinetics observed for smooth catalysts is given hy full circles. The line is a guide for the eye...

There are several examples in the literature of GFC now being utilized for small molecule analysis (17). However, in this case, attempts to obtain monomer concentrations for kinetic modelling were frustrated by irreproducible impurity peak interference with monomer peaks, time varying refractometer responses and insufficient resolution for utilization of a reference peak. This last point meant that injected concentration would have to be extremely reproducible. 

Results are shown in Figures 10 and 11. HPLC is well known as a reproducible and accurate technique for composition measurement From the point of view of kinetic model development however, the following points deserve emphasis. 

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