Abstract
Tracer methods are encountered in many areas of science and engineering. The diversity of their uses is illustrated by measurement of blood flow and capillary permeability of the microcirculation in medicine and by flow visualization in channels and around airplane wings in mechanical and aerospace engineering. Other applications are flow and transport measurements in rivers in hydrology, transport measurements of pollutants in soils in civil engineering, and measurements of spreading of plumes in the atmosphere in environmental engineering. Additional uses involve identification of reaction mechanisms of chemical and catalytic reactions, measurement of diffusion rates, etc. All these methods rely on perturbing the system under investigation and monitoring the system’s response to such perturbations. This response is then interpreted. Some conclusions can be obtained on a model-free basis, others are model dependent.
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References
Danckwerts, P. V, Continuous Flow Systems: Distribution of Residence Times. Chem. Eng. Science 2 (1953) 1.
Levenspiel, O., Chemical Reaction Engineering (New York, Wiley, 2nd ed., 1972).
Froment, G. F and K. B. Bischoff. Chemical Reactor Analysis and Design (New York, Wiley, 1979).
Nauman, E. B and B. A. Buffham. Mixing in Continuous Flow Systems (New York, Wiley, 1983).
Aris, R. The Scope of R.T.D. Theory, Residence Time Distribution Theory in Chemical Engineering. (Petho, A. and R. D. Noble, eds., Weinheim, Verlag-Chemie, 1982). 177
Aris, R. Residence Time Distribution with Many Reactions and in Several Environments, Residence Time Distribution Theory in Chemical Engineering (Petho, A. and R. D. Noble, eds., Weinheim, Verlag-Chemie, 1982).
Brodkey, R. S Fundamentals of Turbulent Motion, Mixing and Kinetics. Chem. Eng. Communications 8 (1981) 1.
Bourne, J. R Micromixing Revisited, ISCRE 8 (Edinburgh, September, 1984).
Nauman, E. B Residence Time Distributions and Micromixing. Chem. Eng. Communications 8 (1981) 53.
Patterson, G. K Application of Turbulence Fundamentals to Reactor Modelling and Scaleup. Chem. Eng. Communications 8 (1981) 25.
Shinnar, R. Tracer Experiments in Chemical Reactor Design, Levich Birthday Conference on Physical Chemistry and Hydrodynamics (Oxford, July, 1977).
Shinnar, R. Use of Residence Time and Contact Time Distributions in Reactor Design, Chemical Reaction Engineering Handbook (Carberry, J. J. and A. Varma, eds., New York, Marcel Dekker, 1985).
Villermaux, J. Mixing in Chemical Reactors. Am. Chem. Soc. Symp. Series 226 (1983) 135.
Waldram, S. P Nonideal Flow in Chemical Reactors, Comprehensive Chemical Kinetics, Vol. 23, Ch. 6 (G. H. Bamford, et. al. eds., Elsevier, Amsterdam, 1985).
Brodkey, R. S, ed. Turbulence in Mixing Operations: Theory and Applications to Mixing and Reaction (New York, Academic Press, 1975).
Hinze, J. O Turbulence (New York, McGraw Hill, 1975).
Danckwerts, P. V Tracers, Residence Times, Mixing and Dispersion. Lecture Notes (Pittsburgh, University of Pittsburgh, 1976).
Gonzales-Fernandez, J. M Theory of the Measurement of the Dispersion of an Indicator in Indicator-Dilution Studies. Circulation Research 10 (1962) 409.
Levenspiel, O. and J. C. R. Turner. The Interpretation of Residence Time Experiments. Chem. Eng. Science 25 (1970) 1605.
Turner, J. C. R The Interpretation of Residence-Time Measurements in Systems with and without Mixing. Chem. Eng. Science 26 (1971) 549.
Buffham, B. A On the Residence Time Distribution for a System with Velocity Profiles in its Connection with the Environment. Chem. Eng. Science 27 (1972) 987.
Villermaux, J Nomenclature and Symbols Recommended by the Working Party on Chemical Reaction Engineering of the E. F. Ch. E., Chem. Eng. Science 35 (1980) 2065.
Sheppard, C. W Basic Principles of the Tracer Method (New York, Wiley, 1962).
Jacquez, J. A Compartmental Analysis in Biology and Medicine (Amsterdam, Elsevier, 1972).
Lassen, N. and W. Perl. Tracer Kinetic Methods in Medical Physiology (New York, Raven, 1979).
Buffham, B. A Internal and External Residence Time Distributions. Chem. Eng. Communications 22 (1983) 105.
Ritchie, B. W and A. H. Tobgy. Residence Time Analysis in Systems Having Many Connections with their Environment. Ind. Eng. Chem. Fundamentals 17 (1978) 287.
Buffham, B. A and H. W. Kropholler. The Washout Curve, Residence Time Distribution and F Curve in Tracer Kinetics. Math. Biosciences 6 (1970) 179.
Zhuang, Z. Model for Flow System Having Multiple Inlet and Outlet Streams. Scientia Simica 24 (1981) 626.
Sherman, H. On the Theory of Indicator-Dilution Methods Under Varying Blood-Flow Conditions. Bull. Math. Biphysics 22 (1960) 417.
Krambeck, F. J., R. Shinnar and S. Katz. Interpretation of Tracer Experiments in Systems with Fluctuating Throughput. Ind. Eng. Chem. Fundamentals 8 (1969) 431.
Krambeck, F. J, R. Shinnar and S. Katz. Stochastic Models for Chemical Reactors. Ind. Eng. Chem. Fundamentals 6 (1967) 276.
Cussler, E. L Diffusion-Mass Transfer in Fluid Systems (Cambridge, Cambridge University Press, 1984).
Bischoff, K. B and E. A. McCracken. Tracer Tests in Flow Systems. Ind. Eng. Chemistry 58 (1966) 18.
Merzkirch, W. Flow Visualization (New York, Academic Press, 1974).
Wang, C. H and D. L. Willis. Radiotracer Methodology in Biological Science (Englewood Cliffs, Prentice Hall, 1965).
Burton, B. S. Take a Look at Nuclear Gauges. Instr. Control Systems. December (1976) 41.
Hines, D. B Some Applications of Radioisotopes in Chemical and Engineering Research, AIChE One Day Symposium, St. Louis, April 1978.
Zwietering, T. N The Degree of Mixing in Continuous Flow Systems. Chem. Eng. Science 11 (1959) 1.
Spalding, D. B. A Note on Mean Residence Times in Steady Flows of Arbitrary Complexity. Chem. Eng. Science 9 (1958) 74.
Stewart, G. N The Pulmonary Circulation Time, the Quantity of Blood in the Lungs and the Output of the Heart. Am. J. Physiology 58 (1921) 20.
Hamilton, W. F, J. W. Moore, J. M. Kinsman and R. G. Spurling. Simultaneous Determination of the Pulmonary and Systematic Circulation Times in Man and of a Figure Related to the Cardiac Output. Am. J. Physiology 84 (1928) 84.
Curl, R. and M. L. McMillan. Accuracy in Residence Time Measurements. AIChE J. 12 (1966) 819.
DudukoviĈ, M. P Tracer Analysis of the Microcirculation (Ph.D. Thesis, Chicago, IIT, 1972).
Hines, D. B Chlor-alkali Plant Mercury Inventory with Mercury-203 Radioisotope. Proc. 15th Meeting Chlorine Plant Managers (The Chlorine Institute, Inc., February, 1972), p.12.
DudukoviĈ, M. P and R. M. Felder. Mixing Effects in Chemical Reactors. AIChE Modular Instruction, Series E. Kinetics, Vol. 4 (New York, AIChE, 1983).
Levich, V. G, V. S. Markin and Y. A. Chrismadzkev. On Hydrodynamic Mixing in a Model of a Porous Medium with Stagnant Zones. Chem. Eng. Science 22 (1967) 1357.
Mills, P. L and M. P. DudukoviĈ. Evaluation of Liquid-Solid Contacting in Trickle-Bed Reactors by Tracer Methods. AIChE J. 27 (198k) 893; AIChE J 28 (1982) 526.
Mills, P. L and M. P. DudukoviĈ. Modified Differential Refractometer for Continuous Liquid-Phase Residence Time Distribution Studies. Ind. Eng. Chem. Fundamentals 18 (1979) 292.
Mills, P. L Catalyst Effectiveness and Solid-liquid Contacting in Trickle-Bed Reactors (D.Sc. Thesis, St. Louis, Washington University, May 1980).
Lapidus, L. Flow Distribution and Diffusion in Fixed-Bed Two-Phase Reactors. Ind. Eng. Chemistry 49 (1957) 1000.
Schiesser, W. E and L. Lapidus. Further Studies of Fluid Flow and Mass Transfer in Trickle-Beds. AIChE J. 7 (1961) 163.
Rothfeld, L. B and J. L. Ralph. Equivalence of Pulse and Step Residence Time Measurements in a Trickle-Phase Bed. AIChE J. 9 (1963) 852.
Awasthi, R. C and K. Vasudeva. On Mean Residence Times in Flow Systems. Chem. Eng. Science 38 (1983) 313.
Naor, P. and R. Shinnar. Representation and Evaluation of Residence Time Distributions. Ind. Eng. Chem. Fundamentals 2 (1963) 278.
Nauman, E. B Nonisothermal Reactors: Theory and Applications of Thermal Time Distribution. Chem. Eng. Science 32 (1977) 359.
Levenspiel, O. The Chemical Reactor Omnibook (Corvallis, Oregon State University Bookstores, 1979).
Wen, C. Y and L. T. Fan. Models for Flow Systems and Chemical Reactors (New York, Marcel Dekker, 1975).
Cholette, A. and L. Cloutier. Mixing Efficiency Determination for Continuous Flow Systems. Can. J. Chem. Engineering, 37 (1953) 105.
Nagata, S. Mixing: Principles and Applications (New York, Halsted Press, 1975).
Corrigan, T. E and W. O. Beavers. Continuous Stirred Tank Reactors. (1968) 1003. Dead Space Interaction in Chem. Eng. Science 23
Norwood, K. W and A. B. Metzner. Flow Patterns and Mixing Rates in Agitated Vessels. AIChE J. 6 (1960) 432.
Gibilaro, L. G The Recycle Flow Mixing Model. Chem. Eng. Science 26 (1971) 299.
Van de Vusse, J. G A New Model for the Stirred Tank. Chem. Eng. Science 17 (1962) 507.
Moo-Young, M. and K. W. Chan. Non-Ideal Flow Parameters for Viscous Fluids Flowing Through Stirred Tanks. Can. J. Chem. Engineering 49 (1971) 187.
Holmes, D. B, R. M. Voncken and J. A. Dekker. Fluid Flow in Turbine-Stirred Baffled Tanks. I. Circulation Time. Chem. Eng. Science 19 (1964) 201.
Voncken, R. M, D. B. Holmes and H. W. den Hartog. Fluid Flow in Turbine-Stirred Baffled Tanks. II. Dispersion During Circulation. Chem. Eng. Science 19 (1964) 209.
Khang, S. J and O. Levenspiel. New Scaleup and Design Method for Stirrer Agitated Batch Mixing Vessels. Chem. Eng. Science 31 (1976) 569.
Rippin, D. W. T The Recycle Reactor as a Model of Incomplete Mixing. Ind. Eng. Chem. Fundamentals 6 (1967) 488.
Fu, B., H. Weinstein, B. Bernstein and A. B. Shaffer. Residence Time Distributions of Recycle Systems — Integral Equation Formulation. Ind. Eng. Chem. Process Design Development 10 (1971) 501.
Buffham, B. A and E. B. Nauman. On the Limiting Form of the Residence Time Distribution for a Constant Volume Recycle System. Chem. Eng. Science 30 (1975) 1519.
Nauman, E. B and B. A. Buffham. Limiting Forms of the Residence Time Distribution for Recycle Systems. Chem. Eng. Science 32 (1977) 1233.
Nauman, E. B and B. A. Buffham. A Note on Residence Time Distributions in Recycle Systems. Chem. Eng. Science 34 (1979) 1057.
Rubinovitch, M. and U. Mann. The Limiting Residence Time Distribution of Continuous Recycle Systems. Chem. Eng. Science. 34 (1979) 1309.
Buffham, B. A and E. B. Nauman. Residence-Time Distribution at High Recycle Ratios. Chem. Eng. Science 39 (1984) 841.
Leitman, R. H and E. N. Ziegler. Stirred Tank Reactor Studies: Part I: Mixing Parameters. Chem. Eng. Journal 2 (1971) 252.
Leitman, R. H and E. N. Ziegler. Stirred Tank Reactor Studies: Part II. Conversion Models. Chem. Eng. Journal 3 (1972) 245.
Hanley, T. R and R. A. Mischke. A Mixing Model for a Continuous Flow Stirred Tank Reactor. Ind. Eng. Chem. Fundamentals 17 (1978) 51.
Spencer, J. L, R. R. Lunt and S. A. Leshaw. Identification of Micromixing Mechanisms in Flow Reactors: Transient Inputs of Reactive Tracers. Ind. Eng. Chem. Fundamentals 19 (1980) 135.
Spencer, J. L and R. R. Lunt. Experimental Characterization of Mixing Mechanisms in Flow Reactors Using Reactive Tracers. Ind. Eng. Chem. Fundamentals 19 (1980) 142.
Lintz, H. G and W. Weber. The Study of Mixing in a Continuous Stirred Tank Reactor Using an Autocatalytic Reaction. Chem. Eng. Science 35 (1980) 203.
Denbigh, K. G, N. Dombrowski, A. J. Kisiel and E. R. Place. The Use of the “Time Reaction” in Residence Time Studies. Chem. Eng. Science 17 (1962) 573.
Danckwerts, P. V and R. A. M. Wilson. Flow Visualization by Means of a Time Reaction. J. Fluid Mechanics 16 (1963) 412.
Castellana, F. S, M. I. Friedman and J. L. Spencer. Characterization of Mixing in Reactor Systems Through Analysis of Regional Tracer Dilution Data Obtained with a Gamma Camera. AIChE Journal 30 (1984) 207.
Mecklenburgh, J. C and S. Hartland. The Theory of Backmixing. (London, Wiley, 1975).
Shah, Y. T, G. J. Stiegel and M. M. Sharma. Backmixing in Gas-Liquid Reactors. AIChE Journal 24 (1978) 369.
Klinkenberg, A. Distribution of Residence Times in a Cascade of Mixed Vessels with Backmixing. Ind. Eng. Chem. Fundamentals 5 (1966) 283.
Hochman, J. M and J. R. McCord. Residence Time Distribution in Recycle Systems with Crossmixing. Chem. Eng. Science 25 (1970) 97.
Bhavaraju, S. M, T. W. F. Russell and H. W. Blanch. The Design of Gas Sparged Devices for Viscous Liquid Systems. AIChE Journal 24 (1978) 454.
Maruyama, T., N. Kamishima and T. Mizuchina. Investigation of Bubble Plume Mixing by Comparison with Liquid Jet Mixing. J. Chem. Eng. Japan 17 (1984) 120.
Levenspiel, O. and K. B. Bischoff. Patterns of Flow in Chemical Process Vessels. Advances in Chemical Engineering, Vol. 4 (Drew, T. B., ed., New York, Academic Press, 1963).
Van der Laan, E. T Notes on the Diffusion-Type Model for the Longitudinal Mixing of Fluids in Flow. Chem. Eng. Science 7 (1958) 187.
Wehner, J. F and R. H. Wilhelm. Boundary Conditions of Flow Reactor. Chem. Eng. Science 6 (1956) 89.
Bischoff, K. B A Note on Boundary Conditions for Flow Reactors. Chem. Eng. Science 16 (1961) 131.
Choi, C. Y and D. D. Perlmutter. A Unified Treatment of the Inlet Boundary Condition for Dispersive Flow Models. Chem. Eng. Science 31 (1976) 250.
Parulekar, S. J and D. Ramkrishna. Analysis of Axially Dispersed Systems with General Boundary Conditions I, II and III. Chem. Eng. Science 39 (1984) 1571, 1581, 1599.
Taylor, G. I Dispersion of Soluble Matter in Solvent Flowing Slowly through a Tube. Proc. Roy. Society (London) A219 (1953) 186.
Taylor, G. I The Dispersion of Matter in Turbulent Flow through a Pipe. Proc. Roy. Society (London) A223 (1954) 446.
Taylor, G. I Diffusion and Mass Transport in Tubes. Proc. Physical Society (London) B67 (1954) 857.
Aris, R. On the Dispersion of a Solute in a Fluid Flowing through a Tube. Proc. Roy. Society A235 (1956) 67.
Koch, D. L and J. F. Brady. Dispersion in Fixed Beds. J. Fluid Mechanics (1985). To appear.
Bischoff, K. B A Note on Gas Dispersion in Packed Beds. Chem. Eng. Science 24 (1969) 607.
Deans, H. A A Mathematical Model for Dispersion in the Direction of Flow in Porous Media. Soc. Petro Eng. Journal 3 (1963) 49.
Hoogendorn, C. J and J. Lips. Axial Mixing of Liquid in Gas-Liquid Flow through Packed Beds. Can. J. Chem. Engineering 43 (1965) 125.
Hochman, J. M and E. Effron. Two-Phase Countercurrent Downflow in Packed Beds. Ind. Eng. Chemistry Fundamentals, 8 (1969) 63.
Buffham, B. A, L. G. Gibilaro and M. N. Rathor. A Probabilistic Time Delay Description of Flow in Packed Beds. AIChE Journal 16 (1970) 218.
Rathor, M. N, L. G. Gibilaro and B. A. Buffham. The Hopping Model for Residence Time Distributions of Systems with Splitting and Merging Streams. AIChE Journal 31 (1985) 330.
Schwartz, J. G and G. W. Roberts. An Evaluation of Models for Liquid Backmixing in. Trickle-Bed Reactors. Ind. Eng. Chem. Process Design Development 12 (1973) 262.
Hinduja, M. J, S. Sundaresan and R. Jackson. A Cross-flow Model of Dispersion in Packed Bed Reactors. AIChE Journal 26 (1980) 274.
Aris, R. Residence Times in Several Environments. Recent Advances in Engineering Analysis of Chemically Reacting Systems. (Doraiswamy, L. V., ed., New Delhi, Wiley Eastern, 1984).
Levenspiel, O. Private Communications. March, 1983.
Shinnar, R., P. Naor and S. Katz. Evaluation of Multiple Tracer Experiments. Chem. Eng. Science 27 (1972) 1627.
Furusawa, T., M. Suzuki and J. M. Smith. Rate Parameters in Heterogeneous Catalysis by Pulse Techniques. Cat. Rev. Sci. Eng. 13 (1976) 43.
McCoy, B. J Approximation of a Heterogeneous Chemical Reaction with a Fluid Phase Reaction. Chem. Eng. Science 39 (1984) 1524.
Weinstein, H. and M. P. DudukoviĈ. Tracer Methods in the Circulation, Topics in Transport Phenomena, Ch. 4 (Gutfinger, C., ed., New York, Hemisphere Pub. Corp. 1975).
Miller, G. A and J. E. Bailey. Some New Results for Chromatographic Kinetics Studies. AIChE Journal 19 (1973) 876.
Shinnar, R. and D. Rumschitzki. The Use of Residence Time Distributions in Heterogeneous Reactor Modeling, Design and Scaleup. 76th AIChE Annual Meeting, San Francisco, November 1984. paper 139b.
Mills, P. L, W. P. Wu and M. P. DudukoviĈ. Tracer Analysis in Systems with Two-Phase Flow. AIChE Journal 25 (1979) 885.
Ramachandran, P. A and J. M. Smith. Dynamics of Three-Phase Slurry Reactors. Chem. Eng. Science 32 (1977) 873.
Ramachandran, P. A and J. M. Smith. Dynamic Behavior of Trickle-Bed Reactors. Chem. Eng. Science 34 (1979) 75.
Ramachandran, P. A and R. V. Chaudhari. Three-Phase Catalytic Reactors. (New York, Gordon & Breach, Pub., 1983).
Schwartz, J. G, E. Weger and M. P. DudukoviĈ. Liquid Holdup and Dispersion in Trickle-Bed Reactors. AIChE Journal 22 (1976) 953.
DudukoviĈ, M. P and P. L. Mills. Contacting and Hydrodynamics in Trickle-Bed Reactors, Encyclopedia of Fluid Mechanics (Cheremisinoff, N. P., ed., New York, Gulf Publ. Corp., 1985).
Sicardi, S., G. Baldi and V. Specchia. Hydrodynamic Models for the Interpretation of the Liquid Flow in Trickle-Bed Reactors. Chem. Eng. Science 35 (1980) 1775.
Eroglu, I. and T. Dogu. Dynamic Analysis of a Trickle-Bed Reactor by Moment Technique. Chem. Eng. Science 38 (1983) 801.
Kan, K. M and P. F. Greenfield. Residence-Time Model for Trickle-Flow Reactors Incorporating Incomplete Mixing in Stagnant Regions. AIChE Journal 29 (1983) 123.
Herskowitz, M. and J. M. Smith. Liquid Distribution in Trickle-Bed Reactors — 2. Tracer Studies. AIChE Journal 24 (1978) 450.
Schwartz, J. G, E. Weger and M. P. DudukoviĈ. A New Tracer Method for Determination of Liquid-Solid Contacting Efficiency in Trickle-Bed Reactors. AIChE Journal 22 (1976) 894.
Colombo, A. J, G. Baldi and S. Sicardi. Solid-Liquid Contacting Effectiveness in Trickle-Bed Reactors. Chem. Eng. Science 31 (1976) 1101.
DudukoviĈ, M. P Catalyst Effectiveness Factor and Contacting Efficiency in Trickle-Bed Reactors. AIChE Journal 23 (1977) 940.
Murphee, E. V, A. Voorhies, Jr. and F. X. Mayer. Application of Contacting Studies to the Analysis of Reactor Performance. Ind. Eng. Chem. Proc. Des. Develop. 3 (1964) 381.
Argo, W. B and D. R. Cova. Longitudinal Mixing in Gas-Sparged Tubular Vessels. Ind. Eng. Chem. Process Des. Develop. 4 (1965) 352.
Bischoff, K. B and J. B. Phillips. Longitudinal Mixing in Orifice Plate Gas-Liquid Reactors. Ind. Eng. Chem. Process Des. Develop. 5 (1966) 416.
Reith, T., S. Renken and B. A. Israel. Gas Holdup and Axial Mixing in Fluid Phase of Bubble Columns. Chem. Eng. Science 23 (1968) 619.
Kunigita, E., M. Ikura and T. Otake. Liquid Behavior in Bubble Column. J. Chem. Eng. Japan 3 (1970) 24.
Ohki, Y. and H. Inoue. Longitudinal Mixing of the Liquid Phase in Bubble Columns. Chem. Eng. Science 25 (1970) 1.
Eissa, S. H, M. M. El-Halwagi and M. Saleh. Axial and Radial Mixing in a Cocurrent Bubble Column. Ind. Eng. Chem. Process Des. Develop. 10 (1971) 31.
Deckwer, W. D, U. Graeser, H. Langemann and Y. Serpemen. Zones of Different Mixing in Liquid Phase Bubble Columns. Chem. Eng. Science 28 (1972) 1972.
Chen, B. H Effects of Liquid Flow on Axial Mixing of Liquid in a Bubble Column. Can. J. Chem. Engineering 50 (1972) 436.
Deckwer, W. D, R. Burckhart and G. Zoll. Mixing and Mass Transfer in Tall Bubble Columns. Chem. Eng. Science 29 (1974) 2177.
Hikita, H. and H. Kikukawa. Liquid-Phase Mixing in Bubble Columns: Effect of Liquid Properties. Chem. Eng. Journal 8 (1974) 191.
Towell, G. D and G. H. Ackerman. Axial Mixing of Liquid and Gas in Large Bubble Reactors. Proc. Symp. Chem. Reaction Engineering (Amsterdam, 1972, pp B3–1–B3–13).
Alexander, B. F and Y. T. Shah. Axial Dispersion Coefficients in Bubble Columns. Chem. Eng. Journal 11 (1976) 153.
Gondo, S., S. Tanaka, K. Kazikuri and K. Kusunoki. Liquid Mixing by Large Gas Bubbles in Bubble Columns. Chem. Eng. Science 28 (1973) 1437.
Eissa, S. H and K. Schügerl. Holdup and Backmixing. Investigations in Cocurrent and Countercurrent Bubble Columns. Chem. Eng. Science 30 (1975) 1251.
Rice, R. G, J. M. I. Tupperainen and R. M. Hedge. Dispersion and Holdup in Bubble Columns — Comparison of Rigid and Flexible Spargers. Can. J. Chem. Engineering 59 (1981) 677.
Field, R. W and J. F. Davidson. Axial Dispersion in Bubble Columns. Trans. Instn. Chem. Engineers 58 (1980) 228.
Kelkar, B. G, S. R. Phulgaonkar and Y. T. Shah. The Effect of Electrolyte Solutions on Hydrodynamic and Backmixing Characteristics in Bubble Columns. Chem. Eng. Journal 27 (1983) 125.
Kelkar, B. G, Y. T. Shah and N. L. Carr. Hydrodynamics and Axial Mixing in a Three Phase Bubble Column — Effects of Slurry Properties. Ind. Eng. Chem. Process Des. Develop. 23 (1984) 308.
Stiegel, G. J and Y. T. Shah. Backmixing and Liquid Holdup in Gas-Liquid Cocurrent Upflow Packed Column. Ind. Eng. Chem. Process Des. Develop. 16 (1977) 37.
Chen, B. H Holdup and Axial Mixing in Bubble Columns Containing Screen Cylinder. Ind. Eng. Chem. Process Des. Devel. 15 (1976) 20.
Shah, Y. T, C. A. Ratway and H. G. Mcilvried. Backmixing Characteristics of a Bubble Column with Vertically Suspended Tubes. Trans. Instn. Chem. Engineers 56 (1978) 107.
Pilhofer, Th., H. F. Bach, and K. H. Mamgartz. Determination of Fluid Dynamic Parameters in Bubble Column Design. ACS Symp. Series 65 (1978) 372.
Deckwer, W. D, K. Nguyen-Tien, B. G. Kelkar and Y. T. Shah. Applicability of Axial Dispersion Model to Analyze Mass Transfer Measurements in Bubble Columns. AIChE Journal 29 (1983) 915.
Vasalos, I. A, E. M. Bild, D. N. Rundell and D. F. Tatterson. Experimental Techniques for Studying the Fluid Dynamics of the H-Coal Reactor. Coal Processing Technology V6 (New York, AIChE J., 1980, pp. 226).
Overcashier, R. H, D. E. Todd and R. B. Olney. Some Effects of Baffles on a Fluidized System. AIChE Journal 5 (1959) 54.
Orcutt, J. C, J. F. Davidson and R. L. Pigford. Reaction Time Distributions in Fluidized Catalytic Reactors. Chem. Engr. Progress Symp. Series No. 38, Vol. 58 (1962) 1.
Yates, J. G and J. A. P. Constans. Residence Time Distributions in a Fluidized Bed in which Gas Adsorption Occurs: Stimulus-Response Experiments. Chem. Eng. Science 28 (1973) 1341.
Nauman, E. B and C. N. Collinge. The Theory of Contact Time Distributions in Gas Fluidized Beds. Chem. Eng. Science 23 (1968) 1309.
Nauman, E. B and C. N. Collinge. Measurement of Contact Time Distribution in Gas Fluidized Beds. Chem. Eng. Science 23 (1968) 1317.
Dohein, M. A and C. N. Collinge. Contact Time Distribution in Fluidized-Bed Reactors, Part I. Measurement at Room and Higher Temperatures. Chem. Eng. Journal 19 (1980) 39.
Dohein, M. A and C. N. Collinge. Contact Time Distribution in Fluidized-Bed Reactors. Part II. Application of Mathematical Models and Parameter Estimation. Chem. Eng. Journal 19 (1980) 47.
Baba, T., M. Nakajima, S. Morooka and H. Matsuyama. New Measuring Syst em for Flow Patterns of Solid Particles in Gas-Solid Fluidized Bed. J. Chem. Eng. Japan 17 (1984) 275.
Rabbits, M. C, G. J. Van Den Houten, D. Glasser and A. W. Bryson. Modeling of Residence Time Distribution in an Entrained Flow Coal Gasification Reactor. Chemsa 9 (1983) 220.
Kato, K., D. Taneda, Y. Sato and M. Maa. Lateral Solid Mixing in a Packed Fluidized Bed. J. Chem. Eng. Japan 17 (1984) 78.
Bauer, W. and J. Werther. Role of Gas Distribution in Fluidized Bed Chemical Reactor Design. Chem. Eng. Communications 18 (1982) 137.
Wippern, D., K. Wittman, J. Kuehne, H. Helmrich and K. Schugerl. Characterization of Fluidized Bed Reactors with Gas Tracer Measurements. Chem. Eng. Communications 10 (1981) 307.
Burghardt, A. and J. M. Smith. Dynamic Response of a Single Catalyst Pellet. Chem. Eng. Science 34 (1979) 267.
DudukoviĈ, M. P An Analytical Solution for the Transient Response in a Diffusion Cell of the Wicke-Kallenbach Type. Chem. Eng. Science 37 (1982) 153.
Dutta, R., B. Croes and R. G. Rinker. Transient Response of Continuous Flow Stirred Reactors Containing Heterogeneous Systems for Catalysis or Sorption. Chem. Eng. Science 38 (1983) 885.
Midoux, N. and J. C. Charpentier. Apparent Diffusivity and Tortuosity in a Liquid Filled Porous Catalyst used for Hydrodesulfurization of Petroleum Products. Chem. Eng. Science 28 (1973) 2108.
Schneider, P. and J. M. Smith. Adsorption Rate Constants from Chromatography. AIChE Journal 14 (1968) 762.
Suzuki, M. and J. M. Smith. Kinetic Studies by Chromatography. Chem. Eng. Science 26 (1971) 221.
Dutta, R. and R. G. Rinker. Transient Response of Three Phase Slurry Reactors. Chem. Eng. Science 39 (1984) 893.
Villermaux, J. Theory of Linear Chromatography, Percolation Processes: Theory and Applications (Rodriguez, A. E. and Toudeur, D., eds., Alphen eau den (Rijn, the Netherlands, Sijthoff & Noordhoff, 1981, p. 83).
Happel, J. Study of Kinetic Structure Using Marked Atoms. Catalysis Reviews 6 (1972) 221.
Bennett, C. O The Transient Method and Elementary Steps in Heterogeneous Catalysis. Catal. Rev. — Sci. Eng. 13 (1976) 121.
Happel, J., I. Suzuki, P. Kokayeff and V. Fthemakis. Multiple Isotope Tracing of Methanation over Nickel Catalyst. J. Catalysis 65 (1980) 59.
Happel, J., H, Y, Cheh, M. Otarad, S. Ozawa, A. J. Severdia, T. Yoshido and V. Fthemakis. Multiple Isotope Tracing of Methanation over Nickel Catalyst II. Deuteromethanes Tracing. J. Catalysis 75 (1982) 314.
Nassar, R., L. T. Fan and J. R. Too. A Stochastic Treatment of Unimolecular Reactions in an Unsteady State Continuous Flow System. Chem. Eng. Science 36 (1981) 1307.
Nassar, R., J. R. Too and L. T. Fan. Stochastic Modeling of Polymerization in a Continuous Flow Reactor. J. Applied Polymer Science 26 (1981) 3745.
Too, J. R, L. T. Fan and R. Nassar. Markov Chain Models of Complex Chemical Reactions in Continuous Flow Reactors.
Fox, R. O and L. T. Fan. A Master Equation Formulation for Stochastic Modeling of Mixing and Chemical Reactions in Inter-Connected Continuous Stirred Tank Reactors. Instn. Chem. Engrs. Symp. Series 87 (1984) 561.
Glasser, D. and R. Jackson. A Generalized Residence Time Distribution Model for a Chemical Reactor. Instn. Chem. Engrs. Symp. Series 87 (1984) 535.
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© 1986 Martinus Nijhoff Publishers, Dordrecht
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Duduković, M.P. (1986). Tracer Methods in Chemical Reactors. Techniques and Applications. In: de Lasa, H.I. (eds) Chemical Reactor Design and Technology. NATO ASI Series, vol 110. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-4400-8_5
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