Mass transfer batch

Interfacial Mass-Transfer Coefficients. Whereas equiHbrium relationships are important in determining the ultimate degree of extraction attainable, in practice the rate of extraction is of equal importance. EquiHbrium is approached asymptotically with increasing contact time in a batch extraction. In continuous extractors the approach to equiHbrium is determined primarily by the residence time, defined as the volume of the phase contact region divided by the volume flow rate of the phases. 

Tank Cells. A direct extension of laboratory beaker cells is represented in the use of plate electrodes immersed into a lined, rectangular tank, which may be fitted with a cover for gas collection or vapor control. The tank cell, which is usually undivided, is used in batch or semibatch operations. The tank cell has the attraction of being both simple to design and usually inexpensive. However, it is not the most suitable for large-scale operation or where forced convection is needed. Rotating cylinders or rotating disks have been used to overcome mass-transfer problems in tank cells. An example for electroorganic synthesis is available (46). 

Design Methods for Turbo-Tray Dryers The heat- and mass-transfer mechanisms are similar to those in batch tray diyers, except that constant turning over and mixing of the solids significantly improves diying rates. Design must usually be based on previous installations or pilot tests by the manufacturer apparent heat-transfer... 

Rate equations are used to describe interphase mass transfer in batch systems, packed beds, and other contacting devices for sorptive processes and are formulated in terms of fundamental transport properties of adsorbent and adsorbate. 

FIG. 16-14 Constant separation factor batch adsorption curves for external mass-transfer control with an infinite fluid volume and n j = 0. 

Batch Stirred Tanks Tanks agitated by coaxial impellers (turbines, paddles, or propellers) are commonly used for batch dissolution of solids in liquids and may be used for leaching fine solids. Insofar as the controlhng rate in the mass transfer is the rate of transfer of mate-... 

Wachi, S. and Jones, A.G., 1991b. Effect of gas-liquid mass transfer on crystal size distribution during the batch precipitation of calcium carbonate. Chemical Engineering Science, 46, 3289-3293. 

The reaction rate ( rco) for a constant volume batch reactor system is equal to the rate of mass transfer (r coy. 

Figure 3.11 illustrates the mass transfer coefficient for batch-grown R. rubrum and was computed with various acetate concentrations at 200 rpm agitation speed, 500 lux light intensity, and 30 °C. As the experiment progressed, there was an increase in the rate of carbon monoxide uptake in the gas phase and a gradual decrease in die partial pressure of carbon monoxide. Also, a decrease in the partial pressure of carbon monoxide was affected by acetate concentration in the culture media. The value of the slope of the straight line increased with the decrease in acetate concentrations, i.e. 2.5 to 1 g-l. The maximum mass transfer coefficient was obtained for 1 g-l 1 acetate concentration (KLa = 4.3-h 1). The decrease in mass transfer coefficient was observed with the increase in acetate concentration. This was due to acetate inhibition on the microbial cell population as acetate concentration increased in the culture media. The minimum KLa was 1.2h 1 at 3g l 1 acetate concentration. 

Heat and mass transfer limitations are rarely important in the laboratory but may emerge upon scaleup. Batch reactors with internal variations in temperature or composition are difficult to analyze and remain a challenge to the chemical reaction engineer. Tests for such problems are considered in Section 1.5. For now, assume an ideal batch reactor with the following characteristics ... 

Many semibatch reactions involve more than one phase and are thus classified as heterogeneous. Examples are aerobic fermentations, where oxygen is supplied continuously to a liquid substrate, and chemical vapor deposition reactors, where gaseous reactants are supplied continuously to a solid substrate. Typically, the overall reaction rate wiU be limited by the rate of interphase mass transfer. Such systems are treated using the methods of Chapters 10 and 11. Occasionally, the reaction will be kinetically limited so that the transferred component saturates the reaction phase. The system can then be treated as a batch reaction, with the concentration of the transferred component being dictated by its solubility. The early stages of a batch fermentation will behave in this fashion, but will shift to a mass transfer limitation as the cell mass and thus the oxygen demand increase. 

Measurements Using Liquid-Phase Reactions. Liquid-phase reactions, and the oxidation of sodium sulfite to sodium sulfate in particular, are sometimes used to determine kiAi. As for the transient method, the system is batch with respect to the liquid phase. Pure oxygen is sparged into the vessel. A pseudo-steady-state results. There is no gas outlet, and the inlet flow rate is adjusted so that the vessel pressure remains constant. Under these circumstances, the inlet flow rate equals the mass transfer rate. Equations (11.5) and (11.12) are combined to give a particularly simple result ... 

Like enzymes, whole cells are sometime immobilized by attachment to a surface or by entrapment within a carrier material. One motivation for this is similar to the motivation for using biomass recycle in a continuous process. The cells are grown under optimal conditions for cell growth but are used at conditions optimized for transformation of substrate. A great variety of reactor types have been proposed including packed beds, fluidized and spouted beds, and air-lift reactors. A semicommercial process for beer used an air-lift reactor to achieve reaction times of 1 day compared with 5-7 days for the normal batch process. Unfortunately, the beer suffered from a mismatched flavour profile that was attributed to mass transfer limitations. 

The reactions are still most often carried out in batch and semi-batch reactors, which implies that time-dependent, dynamic models are required to obtain a realistic description of the process. Diffusion and reaction in porous catalyst layers play a central role. The ultimate goal of the modehng based on the principles of chemical reaction engineering is the intensification of the process by maximizing the yields and selectivities of the desired products and optimizing the conditions for mass transfer. 

In the early part of the reaction the SDR offers no benefit since the reaction is not mass-transfer limited. However, at higher viscosities it was found that a single pass through the SDR at 200 °C gave a similar reduction in acid value (measure of the degree of polymerization) to a batch reaction time of between 40 and 50 min. By recycling the polymer... 

There are several correlations for estimating the film mass transfer coefficient, kf, in a batch system. In this work, we estimated kf from the initial concentration decay curve when the diffusion resistance does not prevail [3]. The value of kf obtained firom the initial concentration decay curve is given in Table 2. In this study, the pore diffusion coefficient. Dp, and surface diffusion coefficient, are estimated by pore diffusion model (PDM) and surface diffusion model (SDM) [4], The estimated values of kf. Dp, and A for the phenoxyacetic acids are listed in Table 2. 

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