Abstract
A probabilistic model describing tracer transport in multiphase spatially inhomogeneous transport (plug-flow) systems is presented. The properties of the trajectories are completely described by a two-component Markov process with absorbing boundaries. The first component is continuous, the second discrete. Infinitesimal conditions are given. Probabilities associated with the process are derived.
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References
O. Levenspiel,Chemical Reaction Engineering, Wiley, New York (1962).
D. M. Himmelblau and B. Bischoff,Process Analysis and Simulation, Wiley, New York (1968).
C. W. Sheppard,Basic Principles of the Tracer Method, Introduction to Mathematical Tracer Kinetics, Wiley, New York (1962).
G. N. Stewart, “Researches on the Circulation Time in Organs and on the Influences which Affect it,”J. Physiol. (London),15:1–30 (1894);22:159–183 (1897–98).
G. N. Stewart, “The Output of the Heart in Dogs,”Am. J. Physiol. 57:27–50 (1921).
R. F. Hamilton, J. W. Moore, J. M. Kinsman, and R. G. Spurling, “Simultaneous Determination of the Pulmonary and Systemic Circulation Times in Mean and of a Figure Related to the Cardiac Output,”Am. J. Physiol. 84:338–344 (1928).
W. F. Hamilton, J. W. Moore, J. M. Kinsman, and R. G. Spurling, “Studies on the Circulation,”Am. J. Physiol. 99:534–551 (1932).
H. Weinstein, B. Fu, R. Acosta, B. Bernstein, and A. B. Shaffer, “Estimation of Circulating Blood Volume from a Tracer Response Curve,”IEEE Trans. on Biomed. Eng. 20 (4):269–277 (1973).
J. B. Bassingthwaighte, T. Strandell, and D. E. Donald, “Estimation of Coronary Blood Flow by Washout of Diffusable Indicators,”Circ. Res. 23:259–278 (1968).
T. R. Harris and E. V. Newman, “An Analysis of Mathematical Models of Circulatory Indicator-dilution Curves,”J. Appl. Physiol. 28:840–850 (1970).
L. B. Wingard, Jr., T. Chorbajian, and S. J. Galla, “Concepts of Residence Time Distribution Applied to the Indicator-Dilution Method,”J. Appl. Physiol. 33:264–275 (1972).
V. E. Sater and O. Levenspiel, “Two-Pase Flow in Packed Beds,”Ind. Eng. Chem. Fund. 5(1):86 (1966).
M. B. Glasser and M. Litt, “A Physical Model of Mixed Phase Flow Through Beds of Porous Particles,”AIChE J. 9(1):103 (1963).
R. Chao and H. E. Hoelscher, “Simultaneous Axial Dispersion and Absorption in a Packed Bed,”AIChE J. 12(2):271 (1966).
J. Dayan and O. Levenspiel, “Longitudinal Dispersion in Packed Beds of Porous Absorbing Solids,”Chem. Eng. Sci. 23:1327 (1968).
F. O. Mixon, D. R. Whitaker, and J. C. Orcutt, “Axial Dispersion and Heat-Transfer in Liquid-Liquid Spray Towers,”AIChE J. 13:21 (1967).
J. Dayan and O. Levenspiel, “RTD for Flow Models with Cross Flow Between, Plug-Flow Regions,” CEP Symp. Series No. 101 (1973), Vol. 66, p. 28.
A. V. Skorokhod, “A Remark on Homogeneous Markov Processes with Discrete Component,”Teor. Verojatnost. i Mat. Statist. Vyp. 1:216–221 (1970).
D. Rappaport and J. Dayan, “Tracer Identiflability of Spatially Inhomogeneous Multiphase Transport Systems,” EE Pub. No. 205, Technion, Israel Institute of Technology, August 1973.
S. Katz and R. Shinnar, “Particulate Methods in Probability Systems,”Ind. Eng. Chem. 61(4) (1969).
I. I. Gikhman and A. V. Skorokhod,Introduction to the Theory of Random Processes, Saunders (1969).
E. B. Dynkin,Markov Processes, Vol. 1, Springer Verlag (1965).
E. A. Coddington and N. Levinsun,Theory of Ordinary Differential Equations, McGraw-Hill (1955).
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Rappaport, D., Dayan, J. A probabilistic model for tracer distribution in multiphase spatially inhomogeneous transport systems. J Stat Phys 11, 481–501 (1974). https://doi.org/10.1007/BF01008891
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DOI: https://doi.org/10.1007/BF01008891