Mass transfer condition

Summarizing, the output of the reactor is an integral over time and over the entire reaction space with all interconnections between different zones of the reactor. Mixing and heat- and mass-transfer conditions are usually different in various zones and the pattern of these differences as well as proportions between size of zones vary with scale. Obviously, the histories of concentrations and temperatures in the zones differ. Whether the integral outputs of laboratory and full-scale reactors differ from each other, depends on the sensitivity of the process to mixing and heat- and mass-transfer conditions. If the sensitivity is low only minor... 

By substituting the well-known Blasius relation for the friction factor, Eq. (45) in Table VII results. Van Shaw et al. (V2) tested this relation by limiting-current measurements on short pipe sections, and found that the Re and (L/d) dependences were in accord with theory. The mass-transfer rates obtained averaged 7% lower than predicted, but in a later publication this was traced to incorrect flow rate calibration. Iribame et al. (110) showed that the Leveque relation is also valid for turbulent mass transfer in falling films, as long as the developing mass-transfer condition is fulfilled (generally expressed as L+ < 103) while Re > 103. The fundamental importance of the Leveque equation for the interpretation of microelectrode measurements is discussed at an earlier point. 

The high surface-to-volume ratio can also significantly improve both thermal and mass transfer conditions within micro-channels in two ways firstly, the convective heat and mass transfers, which take place at the multi-phase interface, are improved via a significant increase in heat and mass transfer area per unit volume. Secondly, heat and mass transfers within a small volume of fluid take a relatively short time to occur, enabling a thermally and diffusively homogeneous state to be reached quickly. The improvement in heat and mass transfer can certainly influence overall reaction rates and, in some cases, product selectivity. Perhaps one of the more profound effects of the efficient heat and mass transfer property of micro-reactors is the ability to carry potentially explosive or highly exothermic reactions in a safe way, due to the relatively small thermal mass and rapid dissipation of heat. 

With this information the maximum flow of energy can be estimated, which can be transported during freezing and main drying at a desired temperature difference between inlet and outlet temperature of the brine at the shelves, e. g. 2000 kj/h at a temperature difference of 3 °C. With this amount of energy approx. 0.7 kg ice could be sublimated per hour. (This estimate gives only the maximum possible sublimation-rate, whether it can be achieved or not depends from heat -and mass transfer conditions in the process (see Section 1.2.1 and Eq. (12)). 

Solvent extraction processes usually run at ambient pressures and temperatures. If higher pressures are applied, it is mostly because a higher extraction temperature is required when equilibrium or mass transfer conditions are more favorable at an elevated temperature. Distillation, on the other hand, is usually carried out at higher temperatures and ambient pressures. To avoid thermal degradation, the pressure sometimes has to be lowered below ambient pressure. Distillation is based on the differences in vapor pressures of the components to be separated, whereas solvent extraction utilizes the differences in intermolecular interactions in the liquid phase. 

Industrially relevant consecutive-competitive reaction schemes on metal catalysts were considered hydrogenation of citral, xylose and lactose. The first case study is relevant for perfumery industry, while the latter ones are used for the production of sweeteners. The catalysts deactivate during the process. The yields of the desired products are steered by mass transfer conditions and the concentration fronts move inside the particles due to catalyst deactivation. The reaction-deactivation-diffusion model was solved and the model was used to predict the behaviours of semi-batch reactors. Depending on the hydrogen concentration level on the catalyst surface, the product distribution can be steered towards isomerization or hydrogenation products. The tool developed in this work can be used for simulation and optimization of stirred tanks in laboratory and industrial scale. 

The gas and liquid can each flow countercurrently, cocurrently downwards or cocurrently upwards. The hydrodynamics and the mass-transfer conditions are different in each of these flow conditions. 

These thin-film evaporators are equipped with rotating elements that create a thin, liquid film of high turbulence along the inner surface of the heated tube (see Figure 1). Consequently, favorable heat and mass-transfer conditions (I), (2) and short residence times result owing to the small holdup (3,4). 

This effect, usually known as feed-side concentration polarization, may become particularly relevant for solutes with a high sorption affinity towards the membrane, which may lead to its depletion near the membrane interface if external mass-transfer conditions are not sufficiently good to guarantee their fast transport from the bulk feed to the interface [32, 36] (see Figure 11.3). As a consequence of their depletion near the interface the driving force for transport, and the resulting partial fluxes, become lower. 

The mass transfer conditions between the fluid phase and fixed phase are assumed to be uniform, as defined by a single mass transport coefficient. Then Eq. (43) should be rewritten as... 

Fig. 4.31. Potential singular point surfaces and stable node bifurcation behavior of reactive membrane separation at different mass transfer conditions B + C< > A Keq = 5 ccba = 5.0, acA = 3.0.

Fig. 5 shows how the discolouration developed in these semibatch experiments is correlated against conversion. At low conversion levels up to 50K, the reaction and mass transfer conditions do not affect the extent of discolouration achieved. Beyond 50K, there is some evidence that under severe conditions (ie. 3011 SO-) the degree of discolouration is accelerating. However for the purposes of initial assessment, the by-product colour can be represented by a parallel reaction where the sulphonation and discolouration reactions have similar activation energies. Brostrom s colour results are different, and shown in Fig. 5 for comparison (15). 

The mechanical stirring usually provides good mass-transfer conditions. The additional use of ultrasound (Compton et al. 1996 De Lima Leite et al. 2002 Ragaini et al. 2001) and microwave devices (Tsai et al. 2002) is reported to have beneficial effects. 

One important oscillating system—namely, the methylamine decomposition on noble metal wires (24,143,227,228)—belongs to this class of ther-mokinetic blocking/reactivation models. This reaction is unique in several ways. It is the only endothermic oscillator (-1-150 kJ/mol), and it is the only unimolecular reaction that displays oscillations caused by sur ce effects. [The oscillating N2O decomposition, reported by Hugo (5) in 1968, does not oscillate because of the instability of the surface reaction, but rather due to the instability of a CSTR when certain heat and mass transfer conditions exist. Any reaction with similar rate and heat effects would oscillate under such circumstances.] This reaction is also the most vigorous oscillator yet observed and displays frequencies of up to 10 Hz and amplitudes approaching 500 K. Moreover, because the reaction oscillates at temperatures of around 1000 K, the oscillations can actually be observed visually as the metal catalyst heats and cools. 

Consider the flow of a fluid over a flat plate of length L with free steam conditions of T, V, and (Fig. 14—45). Noting that convection at the surface (y = 0) is equal to diffusion because of the no-slip condition, the friction, heal transfer, and mass transfer conditions at the surface can be expressed as... 

V. Hatziantoniou, B. Andersson, T. Larsson, N.H. Schodn, L. Carlsson, S. Schwarz, and K.B. Wideen, Preparation, characterization, and testing of a new type of porous catalytic plates usable for liquid-phase hydrogenations at enhanced mass-transfer conditions, Ind. Eng. Chem. Process Des. Dev. 25 143 (1986). 

These mass flows are a function of the oxygen blow rate and conditions as well as gas production, which are constant over the main process time. Towards the end of the process, gas formation depends on carbon concentration and, therefore, the mass transfer conditions change. 

The upper branch of the sigmoidal curve corresponds to mass transfer conditions hence, the wall temperature can be calculated by substituting Eqs. (3) and (4) in Eq. (5) and letting kr oo. Assuming that the resistances to heat and mass transfer can be represented by the film thickness and respectively, we obtain, after some algebra, Eq. (6), where the Lewis number Le represents the ratio of the heat transferring capability of the gas to the rate of diffusion mass transfer. For mixtures of methane and air, Le 1. Since... 

The first is the penetration theory of Higbie (1935). If the liquid immediately adjacent to a rising bubble is assumed to rise with the bubble, i.e., the relative velocity between the bubble and the liquid is 0, the mass transfer conditions are those of unsteady-state molecular diffusion. The mathematical solution of this problem leads to... 

Clarke S.I., Sawistowski H., Phase inversion of stirred liquiddiquid dispersions under mass-transfer conditions, Trans. Instn. Chem. Engrs. 56 (1978), p. 50-55... 

Moving up into the reactor level, effects of convection, dispersion and generation are described in the conservation equations for mass and energy. The momentum balance describes the behavior of pressure. The interface between the reactor and the catalyst level is described by the external mass transfer conditions, most often represented in a Fickian format, i.e., a linear dependence of the rate of mass transfer on the concentration gradient. In cases where an explicit description of mixing and hydrodynamic patterns is required, the simultaneous integration of the Navier-Stokes equations is also conducted at this level. I f the reaction proceeds thermally, the conversion of mass and the temperature effect as a result of it are described here as well. 

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