Mass transfer coefficients fixed beds

The role of external mass transfer resistance can be checked by the estimation of the Biot number and the mass transfer coefficient as described in Appendix 5. For experimental determination of the role of external mass transfer in fixed beds, a simple test is recommended the reaction is carried out in the fixed bed with different amounts of catalyst... 

Average transport coefficients for transfer between the bulk-fluid and particle surface can be correlated in terms of dimensionless groups that characterize the flow conditions. It is common practice to correlate experimental data in terms of y -factors. Usually, the mass transfer coefficient is obtained from the j factor for mass the heat transfer coefficient is obtained from j factor analogy. There have been many experimental studies of mass transfer in fixed-beds and summaries and analyses of the results are available (Whitaker 1972 Dwivedi and Upadhay 1977). For Reynolds numbers greater than 10, the following relationship (Dwivedi and Upadhay 1977) between jo and the Reynolds number represents available data ... 

Mass-Transfer Coefficient Denoted by /c, K, and so on, the mass-transfer coefficient is the ratio of the flux to a concentration (or composition) difference. These coefficients generally represent rates of transfer that are much greater than those that occur by diffusion alone, as a result of convection or turbulence at the interface where mass transfer occurs. There exist several principles that relate that coefficient to the diffusivity and other fluid properties and to the intensity of motion and geometry. Examples that are outlined later are the film theoiy, the surface renewal theoiy, and the penetration the-oiy, all of which pertain to ideahzed cases. For many situations of practical interest like investigating the flow inside tubes and over flat surfaces as well as measuring external flowthrough banks of tubes, in fixed beds of particles, and the like, correlations have been developed that follow the same forms as the above theories. Examples of these are provided in the subsequent section on mass-transfer coefficient correlations. 

It is instructive to consider the relative rates of mass transfer in fixed and fluidized bed reactors. The rapid rate in the fluidized bed is due not so much to the high mass transfer coefficients involved, but to the very large... 

Table 2.2 gives examples of mass transfer coefficients determined from both the single particle and fixed bed models for the evaporation of water from particles of the same diameter and density as in Table 2.1, assuming the diffusivity of water in air to be 3 x 10 m s h Once... 

The second section presents a review of studies concerning counter-currently and co-currently down-flow conditions in fixed bed gas-liquid-solid reactors operating at elevated pressures. The various consequences induced by the presence of elevated pressures are detailed for Trickle Bed Reactors (TBR). Hydrodynamic parameters including flow regimes, two-phase pressure drop and liquid hold-up are examined. The scarce mass transfer data such gas-liquid interfacial area, liquid-side and gas-side mass transfer coefficients are reported. 

Cyclohexene hydrogenation is a well-studied process that serves as model reaction to evaluate performance of gas-liquid reactors because it is a fast process causing mass transfer limitations for many reactors [277,278]. Processing at room temperature and atmospheric pressure reduces the technical expenditure for experiments so that the cyclohexene hydrogenation is accepted as a simple and general method for mass transfer evaluation. Flow-pattern maps and kinetics were determined for conventional fixed-bed reactors as well as overall mass transfer coefficients and energy dissipation. In this way, mass transfer can be analyzed quantitatively for new reactor concepts and processing conditions. Besides mass transfer, heat transfer is an issue, as the reaction is exothermic. Hot spot formation should be suppressed as these would decrease selectivity and catalytic activity [277]. 

Internal recycle reactors are designed so that the relative velocity between the catalyst and the fluid phase is increased without increasing the overall feed and outlet flow rates. This facilitates the interphase heat and mass transfer rates. A typical internal flow recycle stirred reactor design proposed by Berty (1974, 1979) is shown in Fig. 18. This type of reactor is ideally suited for laboratory kinetic studies. The reactor, however, works better at higher pressure than at lower pressure. The other types of internal recycle reactors that can be effectively used for gas-liquid-solid reactions are those with a fixed bed of catalyst in a basket placed at the wall or at the center. Brown (1969) showed that imperfect mixing and heat and mass transfer effects are absent above a stirrer speed of about 2,000 rpm. Some important features of internal recycle reactors are listed in Table XII. The information on gas-liquid and liquid-solid mass transfer coefficients in these reactors is rather limited, and more work in this area is necessary. 

Figure 7.19 represents schematically a way to determine experimentally whether external mass transfer can be neglected. Transfer effects do not occur when the conversion for a given space-time does not depend on the flow rate. The test is not very sensitive, however. This is caused by the small dependence of the mass transfer coefficient on the flow rate at the low Reynolds numbers prevailing in laboratory fixed bed reactors. 

During the extraction an unsteady process prevails. The present paper presents an unsteady state mathematical model for a fixed bed extractor (model 1). The overall mass transfer coefficients were calculated by matching the calculated and experimental values of oil loading in CO2. The results are compared with those obtained by the model developed by Catchpole et al, 1994 (model II). Good agreement between both models results and our experimental measurements were obtained, although the model II allows the best fit over the entire extraction curve. 

Most recently. Kirillov and Nasamanyan15 carried out a very interesting unsteady-state analysis of liquid-solid mass transfer for cocurrent upflow in a fixed-bed reactor. The analysis was compared and verified by the steady-state measurements of liquid-solid mass-transfer coefficients in a 10-cm x 10-cm square column with a height of 50 cm. Three types of packings, 30-mm and 8-mm... 

We see that the mass transfer coefficient increases with the square root of the superficial velocity through the bed. Therefore,/or a fixed concentration, Q, such as that found in a differential reactor, the rate of reaction should vaiy with... 

Because of the analogy between simulated and true counter-current flow, TMB models are also used to design SMB processes. As an example, the transport dispersive model for batch columns can be extended to a TM B model by adding an adsorbent volume flow Vad (Fig. 6.38), which results in a convection term in the mass balance with the velocity uads. Dispersion in the adsorbent phase is neglected because the goal here is to describe a fictitious process and transfer the results to SMB operation. For the same reason, the mass transfer coefficient feeff as well as the fluid dispersion Dax are set equal to values that are valid for fixed beds. 

The pulsed reactor consists of a fixed bed of catalyst pellets through which the reacting fluid moves in pulsating flow. Mass-transfer coefficients are increased because of the pulsating velocity superimposed on the steady flow. For viscous liquids, or any fluid-solid reaction system which has a high extemal-mass-transfer resistance, pulsation may be a practical way to increase the global reaction rate. Biskis and Smith measured mass-transfer coefficients for hydrogen in a-methyl styrene in pulsed flow and found increases up to 80% over steady values. Bradford" found similar results based on data for the dissolution of beds of j9-naphthoI particles in water. 

Air at 294 K and 1 atm enters a fixed-bed adsorber at a flow rate of 0.146 m3/s with a benzene vapor concentration of 29 g/m3. The cylindrical adsorber is 0.61 m in inside diameter and is packed to a height of 1.83 m with 331 kg of silica gel particles having an effective diameter of 2.6 mm and an external porosity of 50%. The adsorption isotherm for benzene has been determined experimentally and found to be linear over the concentration range of interest, given by q = kc, where q is in kg benzene/kg gel, c is in kg benzene/m3 of gas, and k = 4.127 m3 of gas/kg of gel. It has been estimated that the overall volumetric mass-transfer coefficient for the conditions prevailing in the bed is Kc.a = 8.79 s-1. Assuming isothermal and isobaric operation, calculate ... 

Use experimental breakthrough data to estimate the volumetric overall mass-transfer coefficient for fixed-bed adsorption. 

Calculate volumetric overall mass-transfer coefficients in fixed-bed adsorption from correlations for the individual coefficients, and use them for breakthrough predictions. 

The dynamics of the fixed-bed affinity adsorption process were simulated using equations (9-59) to (9-63). The value of the overall volumetric mass-transfer coefficient K(.a was selected by trial and error until a good fit to the experimental data was achieved. Figure 9.13 shows that excellent agreement between the experimental resuls of Camperi et al. (2003) and the model predictions was achieved for Kca = 0.024 s-1. 

Breakthrough curves obtained in a fixed-bed ion exchange process by Pansini et al. (1996) were interpreted by means of the model, the only parameters of which are a solid-liquid and an intra-particle mass transfer coefficient. The experimental results were obtained using a... 

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