Reactor Theory and Applications

Transport Consistent Diffusion Theory Applications to Fuel Storage Pool Criticality  

A computer algorithm has been formulated from ah analytical method which transforms without approximation the general form of the two-dimensiohal (2-D) transport equation into a diffusion-like differential equation. The computational. economy of this procedure is demonstrated in the application of the technique ta the parametric calculations required in determining fuel storage pool -eigenvalues as a function of fuel assembly spacing. 

The development of the transport-diffusion al rithm consists of mathematical operations on the transport equation to obtain a relationship between the net current and flux gradient, formially designated as the. transport diffusion coefficient. The procedure is similar to that of Pomraning with the noteworthy differences that (a) no analytical approximations are required, and, (b) the analytical formulation is constrained to yield a computational algorithm that is consistent with those einpipyed in 2-D discrete ordinates and diffusion theory codes e.g., TWOTRAN (Ref. 2) and 2-DB (Ref. 3). 

To derive the analytical formulation of the transport consistent diffusion coefficient the general form of the multigroup 2-D transport equation is operated on with the integral operator, /(idii, following an expansion of the angular group flux and scattering cross section in terms of spherical harmonica. 

By selecting ai opriate definitions airf term arrangement, the vector equation can be cast te the form 

---

Figure 8.18. Three-zone TAP reactor (D. Constales, G. S. Yablonsky, G. B. Marin and J. T. Gleaves, Multi-zone TAP-reactors theory and application. Ill Multi-response theory and criteria of instantaneousness, Chemical Engineering Science, 59 (2004) 3725).

Clarke,B.L., 1974. Stability analysis of a model reaction network using graph theory. J.Chem.Phys. 60,1493-1501. Constales, D., Yablonsky, G.S., Marin, G.B., Gleaves, J.T., 2001. Multi-zone TAP-reactors theory and application I. 

Three-zone TAP reactor with quadrupole mass spectrometer L one i =/-zone 2 = zone 3 Reprinted from Shekhtman, S.O., Yablonsl, G.S., Chen,S., Cleaves, J.T., 1999. Thin-zoneTAP-reactor—theory and application. Chem. Eng. Sci. 54, 4371—4378, Copyright (1999), with permission from Elsevier. 

Nauman, E. B. Nonisothermal Reactors Theory and Applications of Thermal Time Distribution. Chem. Eng. Science 32 (1977)... 

Chang, H. C., 1983, The domain model in heterogeneous catalysis. Chem. Engng ScL 38,535-546. Cohen, D. S. and Neu, J. C., 1979, Interacting oscillatory chemical reactors. In Bifurcation Theory and Applications in Scientific Disciplines. N.Y. Acad. Sci., New York. 

Villermaux, J. The Chromatographic Reactor in Percolation Processes Theory and Applications, Rodrigues, A. E., Tondeur, D. (Eds.), Sijthoff Noordhoff International Publishers B. V., Alphen aan den Rijn, 1981. 

Gokhman, F., Bergner, A., and Ulbricht, U. (2005) Iron matrix effects on cluster evolution in neutron irradiated reactor steels, 9th Research Workshop Nucleation Theory and Applications, Joint Institute for Nuclear Research, 25 June - 3 July, Dubna, in Schmelzer, J. W., Roepke P., Priezzhev, V. B. (eds.) (2006) Nucleation Theory and Applications, J/VRPwM, 408-419... 

Aris, R., 1979, Chemical reactors and some bifurcation phenomena. In Bijurcation Theory and Applications in Scientific Disciplines, edited by Gurel, O. and Rossler,... 

Asprey, S.P., 1997, Theory and Application of the Temperature-Scanning Plug-Flow Reactor, PhD. Thesis, Queen s University, Kingston, Ontario, Canada. 

L. Ogren, Enzyme Reactors in Analytical Detection Systems. Theory and Applications. Univ. of Lund, Sweden (1981). (Ph.D. Thesis). 

L. B. Miller, Monte Carlo Analysis of Reactivity Coefficients in Fast Reactors General Theory and Applications, ANL-7307 (1967). 

In part I most of the fundamental theory of single phase reactive flows is presented. In part II most of the fundamental theory of multiphase reactive flows is presented. In both parts a few numerical model simulation application examples are given to elucidate the link between theory and applications. In part III the chemical reactor equipment to be modeled are described. Several engineering models are introduced and discussed. A survey of the frequently used numerical methods, algorithms, and schemes is provided. A few practical engineering applications of the modeling tools are presented and discussed. The working principles of several experimental techniques employed in order to get data for model validation are outlined. 

JACKSON, J.D. and HALL, W.B., Influences of buoyancy on heat transfer to fluids flowing in vertical tubes under turbulent condition . Turbulent Forced Convection in Channels and Bundles Theory and Applications to Heat Exchangers and Nuclear Reactors, 2, Advanced Study Institute Book (eds. Kakac, S. and Spalding, D.B.), 613-640, (1979). 

This chapter provides a detailed description of the various commercially available microwave reactors that are dedicated for microwave-assisted organic synthesis. A comprehensive coverage of microwave oven design, applicator theory, and a description of waveguides, magnetrons, and microwave cavities lies beyond the scope of this book. Excellent coverage of these topics can be found elsewhere [1—4]. An overview of experimental, non-commercial microwave reactors has recently been presented by Stuerga and Delmotte [4],... 

A transfer function may not be always analytically invertable, but it has nevertheless value in that the moments of an RTD may be derived from it, notably the variance.. One or two of the moments often are adequate characterizations of an RTD curve and enable useful deductions about the behavior of a vessel as a chemical reactor. Problem P5.02.01 covers the basic theory and P5.02.07 is another application. Figure 5.3 is of a simple process flow diagram, individual transfer functions, and the overall transfer function. 

Houcine I, Plasari E, David R, Villermaux J. Feedstream jet intermittency phenomenon in a continuous stirred tank reactor. Chem Eng J 1999 72 19-29. Zlokarnik M. Dimensional analysis and scale-up in theory and industrial application. In Levin M, ed. Process Scale-Up in the Pharmaceutical Industry. New York Marcel Dekker, 2001. 

Considerations based on the known physical phenomena can guide the choice of catalyst porosity and porous structure, catalyst size and shape and reactor type and size. These considerations apply both to laboratory as well as to large-scale operations. Many comprehensive reviews and good books on the problem of reactor design are available in the literature. The purpose of this book is to teach the reader the mathematical tools that are available for calculating interaction between the transport phenomena and true chemical kinetics, allowing optimization of catalyst performance. The discussed theories are elucidated with examples to provide training for application of the mathematics. 

---