Dispersion, mass transfer and chemical reaction in multiphase contactors: Part I: Theoretical developments

Hatton, T. Alan; Lightfoot, E. N.

doi:10.1002/aic.690300210

Cited by 19 publications

(8 citation statements)

References 18 publications

(24 reference statements)

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“…Early models treated the gas-phase as plug-flow, while the slurry-phase is often assumed to be perfectlymixed [341,342,347,352,356,372]. This latter assumption is inappropriate for simulating small-scale reactors, however, it could be viable for large-scale ones since the liquid-phase backmixing and the dispersion coefficients were reported to increase with reactor diameter [347].…”

Section: Reith Et Al []mentioning

confidence: 98%

“…Due to its simplicity and ease of use, the 1-D axial dispersion model has been widely implemented, however, its validity in describing multi-phase flows with large degrees of backmixing, such as those present in bubble and slurry bubble columns has been scrutinized [339,340], with investigators going as far as advising against the use of the ADM for multiphase systems [341,342]. Hatton and Lightfoot [342] assessed the problem of dispersion and mass transfer from a generalized dispersion framework and showed that simplistic 1-D dispersion models were incapable of describing the dispersion in multiphase systems. Myers et al [343] presented a detailed analysis of the shortcomings of the ADM in bubble columns by comparing it to a two region phenomenological model designated as the slug and cell model, which represents the gas-rich and gas-lean parts of the column.…”

Section: Axial Dispersion Modelmentioning

confidence: 99%

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Fischer–Tropsch Synthesis in Slurry Bubble Column Reactors: Experimental Investigations and Modeling – A Review

Basha

Sehabiague

Abdel‐Wahab

et al. 2015

International Journal of Chemical Reactor Engineering

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This paper presents an extensive review of the kinetics, hydrodynamics, mass transfer, heat transfer and mathematical as well as computational fluid dynamics (CFD) modeling of Low-Temperature Tropsch Synthesis (LTFT) synthesis in Slurry Bubble Column Reactors (SBCRs), with the aim of identifying potential research and development areas in this particular field. The kinetic expressions developed for F-T synthesis over iron and cobalt catalysts along with the water gas shift (WGS) reactions are summarized and compared. The experimental data and empirical correlations to predict the hydrodynamics (gas holdup, Sauter mean bubble diameter, and bubble rise velocity), mass transfer coefficients and heat transfer coefficients are presented. The effects of various operating variables, including pressure, temperature, gas velocity, catalyst concentration, reactor geometry, and reactor internals on the hydrodynamic and transport parameters as well as the performance of SBCRs are discussed. Additionally, modeling efforts of SBCRs, using axial dispersion models (ADM), multiple cell recirculation models (MCCM) and computational fluid dynamics (CFD), are addressed. This review revealed the following:(1) Numerous F-T and WGS kinetic rate expressions are available for cobalt and iron catalysts and one must be careful in selecting the appropriate expressions for LTFT. Iron catalyst suffers from severe attrition and subsequent deactivation in SBCRs and accordingly building a costly catalyst manufacturing facility onsite is required to maintain a steady operation of the F-T reactor;(2) Experimental data on the hydrodynamic and transport parameters at high pressures and temperatures, typical to those of actual F-T synthesis, remain scanty when compared with the plethora of studies conducted using air-water systems in small reactors at ambient conditions; (3) Several empirical correlations for predicting the hydrodynamic and mass as well heat transfer parameters are available and one should select those which consider the reactor diameter, gas mixtures and the potential foamability of the F-T liquids; (4) The effect of cooling internals configuration and sparger design on the hydrodynamic and transport parameters, local turbulence, mixing and catalyst attrition are yet to be seriously addressed; (5) The impact of operating variables on the hydrodynamic and transport parameters as well as the overall performance of the SBCRs should be investigated using actual F-T fluid-solid systems under typical pressures and temperatures using a large-scale reactor ( > 0.15 m ID) in the presence of gas spargers and cooling internals; (6) Significant efforts are still required in order to advance CFD modeling of SBCRs, particularly those pertaining to the relevant closure models, such as drag, lift and turbulence. Also, cooling internals configuration and the design as well as orientation of gas spargers should be accounted for in the CFD modeling; and (7) Proper validations of the CFD formulations using actual systems for F-T SBCR are needed.

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Section: Reith Et Al []mentioning

confidence: 98%

Section: Axial Dispersion Modelmentioning

confidence: 99%

Fischer–Tropsch Synthesis in Slurry Bubble Column Reactors: Experimental Investigations and Modeling – A Review

Basha

Sehabiague

Abdel‐Wahab

et al. 2015

International Journal of Chemical Reactor Engineering

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“…Radially averaged models are awkward for catalytic reactor problems, because the dispersion coefficients depend nonlinearly on the surface kinetics. This dependence has been noted previously for binary systems Gill, 1973, 1974;DeGance and Johns, 1978;Aris, 1980; Hatton and Lightfoot, 1984), and becomes very complicated in multicomponent systems as shown in Eqs. 45-47 and Tables 4-6.…”

Section: Discussionmentioning

confidence: 76%

“…The moments could also be used in principle to calculate the concentration field, though experience suggests that this will not be easy. Hatton and Lightfoot (1984) and by Johns (1985, 1987).…”

Section: ) Of Q(t 2)mentioning

confidence: 94%

Multicomponent reactive dispersion in tubes: Collocation vs. radial averaging

Wang

Stewart

1989

AIChE Journal

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Orthogonal collocation is used to analyze the dispersion and chemical conversion of a multicomponent fluid pulse in a laminar isothermal flow in a catalytic tube. Homogeneous and heterogeneous first-order chemical reactions are included, and a full matrix diffusion law is used. The collocation method represents the dynamics well over wide ranges of system parameters and reaction time. Radial averaging approaches prove less convenient, since the dispersion coefficients thus introduced are complicated functions of time, transport properties and chemical kinetics. IntroductionDispersion effects are widely encountered in chemical reactors and mass transfer systems. In process models, such systems are often treated as one-dimensional by use of transversely averaged mass and energy balances. The local velocity and thermodynamic state in such a model stand for averages over a crosssection of the flow, and the convective dispersion (caused by deviations from these averages) is modelled as enhanced longitudinal diffusion and conduction.The transverse-average approach has been developed extensively for laminar flows in tubes. Taylor (1953) and Aris (1956) derived radially averaged formulas from the long-time asyrnp totes of their two-dimensional problems. Gill and Sankarasubramanian (1 970, 1973, 1974) introduced a set of time-dependent dispersion coefficients Ki(t), and treated first-order reacting systems. Johns (1978, 1979) gave more detailed transient solutions, using a new set of dispersion coefficients & ( t ) based on axial moments of the solute concentration. Multicomponent reacting systems have been studied by DeGance and Johns (1980, 1985, 1987, Aris (1980), andHatton (1981), but only partial results have been obtained.Transversely averaged equations have limited predictive power, since the dispersion coefficients vary with time and with the form of the given problem. The long-time asymptotic forms of these equations are simpler, but also less useful in the presence of fast surface reactions (Aris, 1980). For predictive purposes, an efficient simulation of the process in its full set of dimensions should be preferred. We demonstrate and test the latter approach here, extending the collocation scheme of Wang and Stewart (1983) to reactive multicomponent systems. Problem StatementA multicomponent stream in steady, developed flow through a tube is initially in chemical equilibrium at a uniform composition wo. At time T = 0 a small mass of miscible fluid is injected. The resulting mass-fraction disturbance vector, Au = w -uo, of dimension N is described by the mass-balance equation CollocationAn approximate solution for Aw is sought by orthogonal collocation (Villadsen and Stewart, 1967;Stewart, 1984). The vector Aw in Eqs. 1 -4 is approximated by the function gives a modified differential system, expressible in partitioned matrix form as an anEquation 4 then takes the radially discretized form, various cases of which are analyzed below. This completes the restatement of Eqs. 1-4 as a collocation problem. No...

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“…In the above works, the question as to whether the chemical activity of the transferable solute could have a further influence on the dispersion properties of multiphase contactors was ignored. This situation has since been redressed, and a theoretical analysis of the convective dispersion behavior of reactive, multiphase processes is now available (Hatton and Lightfoot, 1984). The purpose of this paper is to present some specific numerical examples examining the predicted effects of not only chemical reactions, but also of arbitrary transverse concentration averaging policies on the dispersion characteristics of multiphase con tact ors.…”

Section: Introductionmentioning

confidence: 98%

Dispersion, mass transfer and chemical reaction in multiphase contactors: Part II: Numerical examples

Hatton

Lightfoot

1984

AIChE Journal

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which has the following limiting forms when two or more of the parameters a , b and c are equal: has demonstrated that the chemical activity of a solute can have a significant effect on the convective dispersion behavior of multiphase reactors, and that the dispersion parameters estimated using inert tracers for the individual phases may not be representative of the parameters that should be used in the design of reactive systems. Moreover, the use of different transverse averaging procedures for the individual phases can give rise to additional interaction effects between the phases which are not accounted for in the traditional axial dispersion models. The predicted differences in dispersion parameter values depending on whether the solute is inert or not, are in qualitative agreement with published experimental results. T. SCOPEProcedures for the rational design of multiphase contactors should allow for the reduction in mass transfer efficiency which invariably accompanies axial dispersion of the phases. However, a unique characterization of the dispersion processes for any given hydrodynamic situation using the .axial dispersion model does not appear possible, since it has been shown that the rate of interphase mass transfer can modify the effective dispersion processes to a significant degree (Hatton and Lightfoot, 1982). In Part I, an extension of the generalized dispersion theory of Sankarasubramanian (1970, 1971) to multiphase, reactive problems suggested that further modifications to the convective dispersion processes can be anticipated if the solute is chemically active. Moreover, the theoretical results indicate that the use of arbitrary transverse-averaging procedures for the individual phases may give rise to off-diagonal terms in the dispersion parameter matrices, thereby introducing additional interaction effects between the phases not normally accounted for in the axial dispersion model. The purpose of this paper is to report on a numerical study of these effects, for selected parameter values, and thus to complete the study initiated in Part I. CONCLUSIONS AND SIGNIFICANCEThe numerical results presented here confirm that the chemical activity of a solute within a given phase can have a significant effect on the dispersion characteristics of multiphase contactors, and suggest that more attention should be paid to large-scale channelling effects in the design of these contactors.operating under nonisothermal conditions, or for systems ex-

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Dispersion, mass transfer and chemical reaction in multiphase contactors: Part I: Theoretical developments

Cited by 19 publications

References 18 publications

Fischer–Tropsch Synthesis in Slurry Bubble Column Reactors: Experimental Investigations and Modeling – A Review

Fischer–Tropsch Synthesis in Slurry Bubble Column Reactors: Experimental Investigations and Modeling – A Review

Multicomponent reactive dispersion in tubes: Collocation vs. radial averaging

Dispersion, mass transfer and chemical reaction in multiphase contactors: Part II: Numerical examples

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