Kinetics, reactor

The non-equilibrium, short-time behavior of the reactor is described by the conventional reactor Nineties equations 

A a decay constant of delayed neutron precursor group 1, and 

The delayed ueu on constants baire been conqputed for various exposure conditions in N Reactor. Table 7 6.1 gives the various constants for several reactor conditions. 

The delayed neutron fraction is. 693 for green fuel The faction decreases vlth exposure (Pu has a smaller delayed neutron fraction than in the manner 

In the solution of the reactor kinetics equations for short term transients there are two prompt reactivity feedback effects. These are related to the uranium and coolant temperature coefficients 3tenon variation and graphite heating have too long a time constant to affect the short-time kinetics calclatlons  

If one writes the time behavior of all neutrons, h, in a supercritical reactor with no sources as 

Here is taken to be the excess reactivity above delayed critical, /3 is the fraction of neutrons delayed/prompt neutron, and t is the effective lifetime. 

For kgx = a constant (i.e., a step input of reactivity to a reactor in steady operation), one can write a single second order equation  

The term with the negative exponent degenerates rapidly so that after a short time 

The resulting period must be the asymptotic pile period t as designated by the inhour equation, so that a must be identical with l/. a and b are coupled with the coefficients of h and n (Ri and R2) as follows  

The kinetics problems of the second category are concerned with the influence of the reactor temperature on the time-dependent behavior of the neutron flux and on the power generation. The phenomena of interest here are again short-term effects, and the importance of the delayed-neutron groups in establishing dynamically stable systems is discussed. The analytical models used in these treatments draw principally from the so-called Stein model.  

The problems of the third category deal with phenomena that cause long-term variations in the neutron population. These include the production and decay of the principal fission fragments that appear as poisons in the reactor. The effect of these substances upon the reactivity of the system is examined and their practical significance noted. This treatment is concluded with a study of the use of burnout poisons for controlling these long-term changes in reactivity. 

Nearly all the physical situations considered in these analyses refer to bare reactors. This restriction allows solutions to be obtained by the method of separation of variables. Thus the kinetic features of a specific 

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Computer simulation of the reactor kinetic hydrodynamic and transport characteristics reduces dependence on phenomenological representations and idealized models and provides visual representations of reactor performance. Modem quantitative representations of laminar and turbulent flows are combined with finite difference algorithms and other advanced mathematical methods to solve coupled nonlinear differential equations. The speed and reduced cost of computation, and the increased cost of laboratory experimentation, make the former increasingly usehil. 

Spreadsheet Applications. The types of appHcations handled with spreadsheets are a microcosm of the types of problems and situations handled with fuU-blown appHcation programs that are mn on microcomputers, minis, and mainframes and include engineering computations, process simulation, equipment design and rating, process optimization, reactor kinetics—design, cost estimation, feedback control, data analysis, and unsteady-state simulation (eg, batch distillation optimization). 

Cropley, J.B., Systematic Errors in Recycle Reactor Kinetic Studies, Chemical Engineeiing Piogiess, February 1987, 46-51. (Model building, experimental design)... 

In many cases, two identical reaction systems (e.g., a pilot plant scale and a full-scale commercial plant) exhibit different performances. This difference in performance may result from different flow patterns in the reactors, kinetics of the process, catalyst performance, and other extraneous factors. 

Figure 1. Typical reactor temperature profile for continuous addition polymerization a plug-flow tubular reactor. Kinetic parameters for the initiator 1 = 10 ppm Ea = 32.921 kcal/mol In = 26.492 In sec f = 0.5. Reactor parameter [(4hT r)/ (DpCp)] = 5148.2. [(Cp) = heat capacity of the reaction mixture (p) = density of the reaction mixture (h) = overall heat-transfer coefficient (Tf) = reactor jacket temperature (r) = reactor residence time (D) = reactor diameter].

Laidler, K. J., Reactor Kinetics (in two volumes), Pergamon, London, 1963. 

In this article, a dynamic reaction kinetics for propylene epoxidation on Au/Ti02 is presented. Au/Ti02 catalyst is prepared and kinetics experiments are carried out in a tube reactor. Kinetic parameters are determined by fitting the experiments under different temperatures, and the reliability of the proposed kinetics is verified by experiments with different catalyst loading. 

Ref. Catalyst Reactor Kinetic effect Comments and additional data... 

Rogowski, D. F., Marshall, P., and Fontijn, A., High-temperature fast-flow reactor kinetics studies of the reactions of A1 with Cl, A1 with HCl, and AlCl with CI2 over wide temperature ranges, J. Phys. Chem. 93, 1118 (1989). 

Next we need the reaction rates, and chemical reaction is the only aspect that differentiates a multiphase reactor from a separation unit. As with all chemical reactors, kinetics are the most difficult quantities to obtain in describing a reactor accurately. Frequently the rates are... 

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. 

JAEA conducted an improvement of the RELAP5 MOD3 code (US NRC, 1995), the system analysis code originally developed for LWR systems, to extend its applicability to VHTR systems (Takamatsu, 2004). Also, a chemistry model for the IS process was incorporated into the code to evaluate the dynamic characteristics of process heat exchangers in the IS process (Sato, 2007). The code covers reactor power behaviour, thermal-hydraulics of helium gases, thermal-hydraulics of the two-phase steam-water mixture, chemical reactions in the process heat exchangers and control system characteristics. Field equations consist of mass continuity, momentum conservation and energy conservation with a two-fluid model and reactor power is calculated by point reactor kinetics equations. The code was validated by the experimental data obtained by the HTTR operations and mock-up test facility (Takamatsu, 2004 Ohashi, 2006). 

Kipin, J. 961) Physical Fundamentals of Nuclear Reactor Kinetics. Translation from English, Atomizdat, Moscow (in Russian). 

It is obvious that the simulation predicts conversions for below those obtained by Kizer and this cannot be due solely to the neglect of the maleic anhydride degradation. There may be several possible causes for the low predicted values the Orcutt-Davidson PM model may not be sufficiently accurate or the bubble size estimate may be incorrect. Alternatively, neither equation (3) nor (4) correctly describe the reactor kinetics. The number of possibilities may be reduced by considering Figure 4 which plots conversion versus the non-dimensional reaction rate constant, K , with as a parameter. Two possible zones of opera-... 

Figure 3.5. Overall impedance response of a proton exchange membrane (PEM) fuel cell for different cell temperatures, depicted as corresponding values of the real and imaginary parts of the complex impedance (sometimes denoted a Nyquist plot). Each sequence of points represents frequencies ranging from 10 to 10 Hz, with the highest values corresponding to the leftmost points. From M. Ciureanu, S. Mik-hailenko, S. Kaliaguine (2003). PEM fuel cells as membrane reactors kinetic cinalysis by impedance spectroscopy. Catalysis Today 82, 195-206. Used with permission from Elsevier).

Ciureanu, M., Miklailenko, S., Kaliaguine, S. (2003). PEM fuel cell as membrane reactors kinetic analysis by impedance spectroscopy. Catalysis Today 82,195-206. 

A. The cost of building rigorous models of reactor kinetics and hydraulics that give accurate prediction of byproduct yields is usually not justified. The amount of time available for the project is usually insufficient for such models to be built. 

Since the HY at 573 K and 40 bar produces the higher amount of iso-butylbenzene, some other experimental runs have been performed under high pressure on this catalyst at 573, 613 and 643 K, to estimate the activation energy Ea for the three main reactions DEA, ISO and DIS. The runs were carried out at different space velocities to keep the conversion at a value < 10%. Samples of the effluent were collected every 15 minutes in the first three hours on stream. Initial conversion and selectivity were calculated by extrapolating the experimental values at zero time on stream. Initial reaction rates were calculated by the following relationship, typical for the differential reactor kinetic data ... 

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