Abstract
Convective transport phenomena can be viewed as propagation of waves. For such a purpose, a wave is defined as a variation of the values of dependent variables, usually concentrations, temperature, pressure, etc. If the species involved affect one another’s behavior, as is usually the case, the waves are nonlinear (that is, obey nonlinear differential equations). Examples include multicomponent fixed-bed adsorption and ion exchange (Helfferich and Klein, 1970; Rhee et al., 1970, 1986; Vermeulen et al., 1984; Ruthven, 1984), preparative chromatography (Helfferich and James, 1970; Rhee and Amundson, 1982; Frenz and Horvath, 1985), enhanced oil recovery (Welge, 1952; Helfferich, 1981; Hirasaki, 1981; Orr and Taber, 1984; Lake, 1989), leach mining (Walsh et al., 1984), transport with precipitation and dissolution (Bryant et al., 1986, 1987; Novak et al., 1988; Helfferich, 1989a), sedimentation (Kynch, 1952; Wallis G, 1969), travel of disturbances through chemical equipment that is otherwise at equilibrium or steady state (Hwang and Helfferich, 1989), and traffic flow (Whitham, 1974; Tondeur, 1987a). Migration and fate of pollutants in geological formations, especially in aquifers, also is a phenomenon of this type, if a very complex one owing to the irregular, three-dimensional geometry and the usually highly nonuniform permeability of the medium in which it occurs, to the nonuniformity and irregular distribution of soil components that interact with the pollutants, and to chemical reactions which the pollutants may undergo.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Aerivos A (1956) Method of characteristics technique. Application to heat and mass transfer problems. Ind Eng Chem 48:703–710.
Bryant SL, Schechter RS, Lake LW (1986) Interaction of precipitation/dissolution waves and ion exchange in flow through permeable media. AIChE J 32:751–764.
Bryant SL, Schechter RS, Lake LW (1987) Mineral sequences in precipitation/dissolution waves. AIChE J 33:1271–1287.
Buckley SE, Leverett MC (1942) Mechanism of fluid displacement in sands. Trans AIME 146:107–116.
Frenz J, Horvath C (1985) High performance displacement chromatography: Calculation and experimental verification of zone development. AIChE J 31:400–409.
Helfferich F, James DB (1970) An equilibrium theory for rare-earth separation by displacement development. J Chromatogr 46:1–28.
Helfferich F, Klein G (1970) Multicomponent chromatography. Dekker, New York (out of print, available from University Microfilms, Ann Arbor MI, USA).
Helfferich FG (1981) Theory of multicomponent, multiphase displacement in porous media. SPE J 21:51–62.
Helfferich FG (1982) Generalized Welge construction for two-phase flow in porous media with limited miscibility. SPE 9730, presented at SPE Meeting, New Orleans, LA.
Helfferich FG (1984) Conceptual view of column behavior in multicomponent adsorption and ion-exchange systems. AIChE Symp Ser 80 No 233 1–13.
Helfferich FG (1986) Multicomponent wave propagation: Attainment of coherence from arbitrary starting conditions. J Chromatogr 44:275–285.
Helfferich FG (1989a) The theory of precipitation/dissolution waves. AIChE J 35:75–87.
Helfferich FG (1989b) Coherence: power and challenge of a new concept, in Keller GE II, Yang RT (eds) New directions in sorption technology. Butterworths, Boston, Chap 1.
Hirasaki GJ (1981) Application of the theory of multicomponent, multiphase displacement to three-component, two-phase surfactant flooding. SPE J 21:191–204.
Hwang Y-L, Helfferich FG, Leu W-J (1988) Multicomponent equilibrium theory for ion-exchange columns involving reactions. AIChE J 34: 1615–1626.
Hwang Y-L, Helfferich FG (1989) Dynamics of continuous countercurrent mass-transfer processes. III. Multicomponent systems. Chem Eng Sci 44:1547–1568.
Kynch GJ (1952) A theory of sedimentation. Trans Faraday Soc 48:166–176.
Landau LD, Lifshitz EM (1959) Fluid mechanics. Pergamon, London.
Lake LW (1989) Enhanced oil recovery. Prentice Hall, Englewood Cliffs NJ, Chap 5.
Novak CF, Schechter RS, Lake LW (1988) Rule-based mineral sequences in geochemical flow processes. AIChE J 34:1607–1614.
Orr FM Jr, Taber JJ (1984) Use of carbon dioxide in enhanced oil recovery. Science 244:536–539.
Rhee H-K, Aris R, Amundson NR (1970) On the theory of multicomponent chromatography. Phil Trans Roy Soc Lond 267A:419–455.
Rhee H-K, Amundson NR (1982) Analysis of multicomponent separation by displacement development. AIChE J 28:423–433.
Rhee H-K, Aris R, Amundson NR (1986) First-order partial differential equations, vol 1. Prentice Hall, Englewood Cliffs NJ.
Ruthven DM (1984) Principles of adsorption & adsorption processes. Wiley, New York, Chap 9.
Schweich D, Villermaux J, Sardin M (1980) An introduction to the nonlinear theory of adsorptive reactors. AIchE J 26:477–486.
Tondeur D (1987a) Unifying concepts in non-linear unsteady processes. Part I: Solitary travelling waves. Chem Eng Process 21:167–178.
Tondeur D (1987b) Unifying concepts in non-linear unsteady processes. Part II: Multi-component waves, competition and diffusion. Chem Eng Process 22:91–105.
Vermulen T, LeVan MD, Hiester NK, Klein G (1984) Adsorption and Ion Exchange. In: Perry RH, Green DW, Maloney JO (eds) Chemical Engineers’ Handbook, 5th edn., Sec 16. McGraw-Hill, New York.
Wallis G (1969) One-dimensional two-phase flow. McGraw-Hill, New York.
Walsh MP, Bryant SL, Schechter RS, Lake LW (1984) Precipitation and dissolution of solids attending flow through porous media. AIChE J 30:317–328.
Welge HJ (1952) A simplified method for computing oil recovery by gas or water drive, Trans AIME 195:91–98.
Whitham GB (1974) Linear and nonlinear waves. Wiley, New York.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1993 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Helfferich, F.G. (1993). Multicomponent Wave Propagation: The Coherence Principle. An Introduction. In: Petruzzelli, D., Helfferich, F.G. (eds) Migration and Fate of Pollutants in Soils and Subsoils. NATO ASI Series, vol 32. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-77862-9_11
Download citation
DOI: https://doi.org/10.1007/978-3-642-77862-9_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-77864-3
Online ISBN: 978-3-642-77862-9
eBook Packages: Springer Book Archive