Nonequilibrium effects in fixed-bed interstitial fluid dispersion

Alexandre E. Kronberg, K.R. Westerterp

    Research output: Contribution to journalArticleAcademic

    14 Citations (Scopus)

    Abstract

    Continuum models for the role of the interstitial fluid with respect to mass and heat dispersion in a fixed bed are discussed. It is argued that the departures from local equilibrium and not the concentration and temperature gradients as such should be considered as the driving forces for mass and heat dispersion fluxes. This general principle results in a new two-dimensional, continuum model for dispersion in the fluid flowing through a packed bed. An essential feature of the model is that mass and heat dispersion flux vectors are taken to be state variables additional to concentration and temperature; their values characterize the departures from local equilibrium. The differential equations for the dispersion model are of the hyperbolic type and they require fundamentally different boundary conditions compared to the usual conditions for the conventionally used diffusion type models. The new model avoids the physical drawbacks inherent to the diffusion models. It provides a new physical interpretation of the scatter in point temperature measurements and of the temperature drop observed near the reactor wall under conditions of heat transfer through the wall. A part of the temperature drop and the temperature scatter are direct consequences of the macroscopic local thermal nonequilibrium state of the fluid. The results predicted by the new model and diffusion model are essentially equivalent in case of slow processes in reactors with large tube-to-particle diameter ratios. Otherwise the diffusion model does not have a solid physical basis and may not be valid for predictive purposes because of the influence of chemical reaction on the transport parameters.
    Original languageUndefined
    Pages (from-to)3977-3993
    JournalChemical engineering science
    Volume54
    Issue number18
    DOIs
    Publication statusPublished - 1999

    Keywords

    • Diffusion type models
    • IR-74011
    • Radial dispersion
    • Fixed-bed reactors
    • Modeling
    • Axial dispersion
    • Boundary conditions

    Cite this

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    title = "Nonequilibrium effects in fixed-bed interstitial fluid dispersion",
    abstract = "Continuum models for the role of the interstitial fluid with respect to mass and heat dispersion in a fixed bed are discussed. It is argued that the departures from local equilibrium and not the concentration and temperature gradients as such should be considered as the driving forces for mass and heat dispersion fluxes. This general principle results in a new two-dimensional, continuum model for dispersion in the fluid flowing through a packed bed. An essential feature of the model is that mass and heat dispersion flux vectors are taken to be state variables additional to concentration and temperature; their values characterize the departures from local equilibrium. The differential equations for the dispersion model are of the hyperbolic type and they require fundamentally different boundary conditions compared to the usual conditions for the conventionally used diffusion type models. The new model avoids the physical drawbacks inherent to the diffusion models. It provides a new physical interpretation of the scatter in point temperature measurements and of the temperature drop observed near the reactor wall under conditions of heat transfer through the wall. A part of the temperature drop and the temperature scatter are direct consequences of the macroscopic local thermal nonequilibrium state of the fluid. The results predicted by the new model and diffusion model are essentially equivalent in case of slow processes in reactors with large tube-to-particle diameter ratios. Otherwise the diffusion model does not have a solid physical basis and may not be valid for predictive purposes because of the influence of chemical reaction on the transport parameters.",
    keywords = "Diffusion type models, IR-74011, Radial dispersion, Fixed-bed reactors, Modeling, Axial dispersion, Boundary conditions",
    author = "Kronberg, {Alexandre E.} and K.R. Westerterp",
    year = "1999",
    doi = "10.1016/S0009-2509(99)00094-9",
    language = "Undefined",
    volume = "54",
    pages = "3977--3993",
    journal = "Chemical engineering science",
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    }

    Nonequilibrium effects in fixed-bed interstitial fluid dispersion. / Kronberg, Alexandre E.; Westerterp, K.R.

    In: Chemical engineering science, Vol. 54, No. 18, 1999, p. 3977-3993.

    Research output: Contribution to journalArticleAcademic

    TY - JOUR

    T1 - Nonequilibrium effects in fixed-bed interstitial fluid dispersion

    AU - Kronberg, Alexandre E.

    AU - Westerterp, K.R.

    PY - 1999

    Y1 - 1999

    N2 - Continuum models for the role of the interstitial fluid with respect to mass and heat dispersion in a fixed bed are discussed. It is argued that the departures from local equilibrium and not the concentration and temperature gradients as such should be considered as the driving forces for mass and heat dispersion fluxes. This general principle results in a new two-dimensional, continuum model for dispersion in the fluid flowing through a packed bed. An essential feature of the model is that mass and heat dispersion flux vectors are taken to be state variables additional to concentration and temperature; their values characterize the departures from local equilibrium. The differential equations for the dispersion model are of the hyperbolic type and they require fundamentally different boundary conditions compared to the usual conditions for the conventionally used diffusion type models. The new model avoids the physical drawbacks inherent to the diffusion models. It provides a new physical interpretation of the scatter in point temperature measurements and of the temperature drop observed near the reactor wall under conditions of heat transfer through the wall. A part of the temperature drop and the temperature scatter are direct consequences of the macroscopic local thermal nonequilibrium state of the fluid. The results predicted by the new model and diffusion model are essentially equivalent in case of slow processes in reactors with large tube-to-particle diameter ratios. Otherwise the diffusion model does not have a solid physical basis and may not be valid for predictive purposes because of the influence of chemical reaction on the transport parameters.

    AB - Continuum models for the role of the interstitial fluid with respect to mass and heat dispersion in a fixed bed are discussed. It is argued that the departures from local equilibrium and not the concentration and temperature gradients as such should be considered as the driving forces for mass and heat dispersion fluxes. This general principle results in a new two-dimensional, continuum model for dispersion in the fluid flowing through a packed bed. An essential feature of the model is that mass and heat dispersion flux vectors are taken to be state variables additional to concentration and temperature; their values characterize the departures from local equilibrium. The differential equations for the dispersion model are of the hyperbolic type and they require fundamentally different boundary conditions compared to the usual conditions for the conventionally used diffusion type models. The new model avoids the physical drawbacks inherent to the diffusion models. It provides a new physical interpretation of the scatter in point temperature measurements and of the temperature drop observed near the reactor wall under conditions of heat transfer through the wall. A part of the temperature drop and the temperature scatter are direct consequences of the macroscopic local thermal nonequilibrium state of the fluid. The results predicted by the new model and diffusion model are essentially equivalent in case of slow processes in reactors with large tube-to-particle diameter ratios. Otherwise the diffusion model does not have a solid physical basis and may not be valid for predictive purposes because of the influence of chemical reaction on the transport parameters.

    KW - Diffusion type models

    KW - IR-74011

    KW - Radial dispersion

    KW - Fixed-bed reactors

    KW - Modeling

    KW - Axial dispersion

    KW - Boundary conditions

    U2 - 10.1016/S0009-2509(99)00094-9

    DO - 10.1016/S0009-2509(99)00094-9

    M3 - Article

    VL - 54

    SP - 3977

    EP - 3993

    JO - Chemical engineering science

    JF - Chemical engineering science

    SN - 0009-2509

    IS - 18

    ER -