Mass transfer axial backmixing

Axial dispersion (sometimes referred to as backmixing) is a spreading of the concentration profile in the axial direction due to flow variations within the adsorbent bed (see the pulse analysis section in Appendix C). This effect can also contribute to the spreading of the mass transfer zone. 

The determination of the driving force for the interfacial mass transfer is very difficult in extraction columns since no pure plug flow exists within the column This is one of the most important differences between gas-liquid and liquid-Uquid contactors. Because of the small density differences in liquid-liquid systems there exists a relatively high rate of axial backmixing of dispersed as well as of continuous phase. Backmixing reduces the concentration differences along the column height. 

Mass transfer rates in gas-flowing solids-fixed bed contactors are expected to be high, according to fluid dynamics and heat transfer behavior. Somewhat lower values of mass transfer coefficients than those expected were reported in the literature [6,35-37]. The reasons for that are the effects of segregation as well as strong influence of axial backmixing. Apart from this, mass transfer rates depend on size and structure (porosity) of flowing solids [36]. 

Unlike the previous analysis (38), the boundary conditions were properly treated as dependent variables found by taking account of film and bulk reaction balanced with the input and output flows and mass transfer fluxes across a tray. The approach (39) involved perfect backmixing of the liquid, but with provision of the possibility of axial mixing in the gas phase being represented by staging of backmixed zones. In practise though, the authors claimed that a single gas zone was sufficiently accurate. 

Axial dispersion or backmixing " can make a major contribution to the mass transfer rate in liquid-phase adsorption and cannot be ignored. This is especially true at low Reynolds numbers. 

Bubble columns. Tracers are used in bubble columns and gas-sparged slurry reactors mainly to determine the backmixing parameters of the liquid phase and/or gas-liquid or liquid-solid mass transfer parameters. They can be used for evaluation of holdup along the lines reviewed in the previous Section 6.2.1. However, there are simpler means of evaluating holdup in bubble columns, e.g. monitoring the difference in liquid level with gas and without gas flow. Numerous liquid phase tracer studies of backmixing have been conducted (132-149). Steady-state or continuous tracer inputs (132,134,140,142) as well as transient studies with pulse inputs (136,141,142,146) were used. Salts such as KC Jl or NaCil, sulfuric acid and dyes were employed as tracers. Electroconductivity detectors and spectrophotometers were used for tracer detection. The interpretation of results relied on the axial dispersion model. Various correlations for the dispersion... 

Models of BCR can be developed on the basis of various view points. The mathematical structure of the model equations is mainly determined by the residence time distribution of the phases, the reaction kinetics, the number of reactive species involved in the process, and the absorption-reaction regime (slow or fast reaction in comparison to mass transfer rate). One can anticipate that the gas phase as well as the liquid phase can be either completely backmixed (CSTR), partially mixed, as described by the axial dispersion model (ADM), or unmixed (PFR). Thus, it is possible to construct a model matrix as shown in Fig. 3. This matrix refers only to the gaseous key reactant (A) which is subjected to interphase mass transfer and undergoes chemical reaction in the liquid phase. The mass balances of the gaseous reactant A are the starting point of the model development. By solving the mass balances for A alone, it is often possible to calculate conversions and space-time-yields of the other reactive species which are only present in the liquid phase. Heat effects can be estimated, as well. It is, however, assumed that the temperature is constant throughout the reactor volume. Hence, isothermal models can be applied. 

The overall rate of mass transfer of adsorbate in the bed is affected by external transport from the bulk of the gas to the external surfaces of the adsorbent particles, axial dispersion and backmixing in the gas phase, and internal transport within the pores. External transport can be correlated by equations similar to those used for mass transfer in packed absorption columns, such as the Ranz-Marshall (1952) equation ... 

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