Batch mass transfer coefficient

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. 

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. 

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. 

In this case, the material balance in the liquid phase (3.238) is not applicable as both reactants are gases. Furthermore, as in sluny bubble columns, if the liquid is batch, the overall rate based on the bulk gas-phase concentration is used and the overall mass-transfer coefficient K° is found in the solution of the model (Chapter 5). 

The importance of a correct evaluation of kLa(03) or kla 02) was confirmed in a study on the simulation of (semi-)batch ozonation of phenol (Gurol and Singer, 1983). It was shown that a close match between the measured and the calculated data was only obtained when kLa(02) was measured as a function of the residual phenol concentration. The oxygen mass transfer coefficient was observed to change from kLa(02) = 0.049 s 1 at c(M) = 50 mg IF1 phenol to kLa(02) = 0.021 s- at c(M) = 5.0 mg L 1 phenol. 

For example, Beltran and Alvarez (1996) successfully applied a semi-batch agitated cell for the determination of kL k,a, and the rate constants of synthetic dyes, which react very fast with molecular ozone (direct reaction, kD = 5 105 to 1 108 L mol-1 s l). In conventional stirred tank reactors operated in the semi-batch mode the mass transfer coefficient for ozone kLa(03) was determined from an instantaneous reaction of ozone and 4-nitrophenol (Beltran et al., 1992 a) as well as ozone and resorchinol (l,3-c//hydroxybenzene) or phloroglucinol... 

Bacterial inactivation is achieved by CO2 absorption in the liquid phase, even though the reason why it happens is still not clear. In this respect, batch- and semi-continuous operating modes are substantially different. In the batch system the residence time, i.e., the time of contact between gas- and liquid phase, must be sufficient to allow the diffusion of CO2 in the liquid, and is therefore a fundamental parameter to assure a desired efficiency. In the semi-continuous system the contact between the phases is localized in the surface of the moving micro-bubbles. In this second case, the efficiency of the process is influenced by temperature, pressure, gas flux, bubble diameter, and other parameters that modify the value of the mass-transfer coefficient. Therefore, it is not correct to use the residence time as a key parameter in the semi-continuous process. In fact, a remarkable microbial inactivation is reached even with an exposure time of 0 min (i.e., pressurizing and immediately depressurizing the system) these two steps are sufficient to allow CO2 to diffuse through the liquid phase. 

In this study, the effects of cosolvent (EtOH) addition on the solubilization and recovery of PCE by a nonionic surfactant (Tween 80) was evaluated using a combination of batch, column and 2-D box studies. Batch results demonstrated that the addition of 5% and 10% EtOH increased the solubilization capacity of Tween 80 from 0.69 g PCE/g surfactant to 1.09 g PCE/g surfactant. For a 4% Tween 80 solution, this translates into a solubility enhancement of more than 50%, from 26,900 mg/L to 42,300. mg/L. When the surfactant formulations were flushed through soil columns containing residual PCE, effluent concentration data clearly showed that PCE solubilization was rate-limited, regardless of the EtOH concentration. Using analytical solutions to the 1-D ADR equation, effective mass transfer coefficients (Ke) were obtained from the effluent concentration data for both steady-state (A e ) and no flow conditions The addition of EtOH had... 

This model was applied to the same data for batch and flowthrough systems with and without acid addition as for the previous two models, and some of the xylan conversion predictions calculated from the data and concentration predictions via Eq. 8 are summarized in Figs. 5 and 6 for batch and flowthrough systems, respectively. Tables 4 and 2 present the parameters and the SSE values for the branched pore model, respectively. Overall, although some data are better matched than others, hemicellulose hydrolysis models based on mass transfer alone can predict performance in batch and flow systems as well as, if not better than, reaction-only models. In addition, the changes in mass transfer coefficient with flow are consistent with expectations for a mass transfer model but not for strictly a chemical reaction. 

This preliminary study suggests that mass transfer models could describe many features of xylan hydrolysis with accuracy similar to that of conventional first-order reaction-only models that have been long used to describe such systems. For example, a simple leaching model can describe release of xylan into solution as the product of a concentration gradient times a mass transfer coefficient. This model predicts that flowthrough operation could improve xylan release compared to a batch system by reducing the concentration in solution and thereby increasing the concen-... 

External mass transfer limitations, which cause a decrease in both the reaction rate and selectivity, have to be avoided. As in the batch reactor, there is a simple experimental test in order to verify the absence of these transport limitations in isothermal operations. The mass transfer coefficient increases with the fluid velocity in the catalyst bed. Therefore, when the flow rate and amount of catalyst are simultaneously changed while keeping their ratio constant (which is proportional to the contact time), identical conversion values should be found for flow rate high enough to avoid external mass transfer limitations.[15]... 

This example illustrates the distillation of a binary mixture in an open-batch distillery with flowing sweep gas and pervaporation by having a porous plate floating on top of the liquid hold up, as shown in Fig. 4.20. The porous plate was made from inert sintered metal with various pore sizes between 100 and 1 mfi, and had a thickness of 1 mm. The porosity was 40 % and the tortuosity factor was about 2. This results in an effective liquid phase mass transfer coefficient of about hiq = 2 X 10-7 m s-i, which results in Kiiq = 1.9 X 10 22. Therefore, one would expect the distillation process to be nonselective - that is, Si = xi - xi = 0. 

This gives rise to a warning In feasibility studies for an open batch distillation process certain assumptions are made as to the heating policy (see e.g. Ref. [7]). Since the ratio of the evaporation velocity to the liquid phase mass transfer coefficient uiiq/knq also depends on the heating policy , one must ensure that this ratio is sufficiently low otherwise the composition of the reactive arheotrope will also depend on the heating policy. ... 

As demonstrated by means of residue curve analysis, selective mass transfer through a membrane has a significant effect on the location of the singular points of a batch reactive separation process. The singular points are shifted, and thereby the topology of the residue curve maps can change dramatically. Depending on the structure of the matrix of effective membrane mass transfer coefficients, the attainable product compositions are shifted to a desired or to an undesired direction. 

Enantioselectivity was roughly the same for the three reactors, being 80-90 and 62-65% for the Rh/Josiphos and Rh/Diop catalysts, respectively [266]. Conversion was very different. For fixed reaction time, the batch reactor and the falling-film microreactor had higher conversions than the Caroussel reactor. This was indicative of operation under mass transfer regime in the latter. On the basis of these data, it was concluded that the mass transfer coefficients kya of the helical falling-film microreactor are in between the boundaries given by the known kta values of 1-2 s 1 for small batch reactors and about 0.01 s-1 for the Caroussel reactor. 

The experimental technique involves batch gas absorption (by surface aeration) in a liquid. The pressure of the enclosed gas phase in the reactor decreases with time because of the absorption. This decrease in pressure with time allows the estimation of the mass-transfer rate and the volumetric mass-transfer coefficient, kLaL. The total pressure decrease until equilibrium is reached gives the equilibrium solubility C. The relevant equations for the calculations of C and kLaL are derived by Albal et al. (1983), Deimling et al. (1985), and Karandikar et al. (1986). These can be expressed as... 

In a batch slurry reactor, the liquid-solid mass-transfer coefficient can be measured by dissolving a sparingly soluble solid in liquid. The concentration of dissolved solid in liquid (Bt) can be measured as a function of time, preferably by a continuous analytical device. Systems such as the dissolution of benzoic acid, jS-naphthol, naphthalene, or KMn04 in water can be used. A plot of B( as a function of time and the slope of such plot at time t = 0 can give ks as... 

For a semi-batch operation, the liquid-solid mass-transfer coefficient can also be obtained by monitoring a reaction between the dissolving solid B and a liquid reactant C. If this reaction is instantaneous, the enhancement factor for the reaction is... 

The physical methods for the measurement of kLaL in batch, semi-batch, and continuous systems described earlier are accurate. The main limitation for the semi-batch and continuous systems is the availability of the analytical technique for the measurement of the gas concentration in the liquid phase. For gas-liquid-solid systems, Eq. (9.41) can be used to measure both kt and kL simultaneously. The liquid-solid mass-transfer coefficient can also be measured using the method of Ruether and Puri (1973) or the physical methods outlined earlier. 

In these equations, COD (t) is the chemical oxygen demand at time t (mol 02 m-3), I is the current intensity (A), F is the Faraday constant (96,487C mol-1), apPi is the applied current density (Am-2), km the mass-transfer coefficient (ms-1), and ICE is the instantaneous current efficiency. For a typical-batch electrochemical... 

During a typical batch electrolysis, the minimal COD value can be estimated (CODfe min = 4.25mmol dm-3 or 136ppm) by assuming a typical value of minimal hydroxyl production current density (iu,mm = 5.0mA cm-2), and a characteristics value of mass-transfer coefficient (km = 3 x 10 s m s ). The obtained minimal COD value is higher than the final treatment value that is usually required (CODf). Consequently, it can be stated that the electrochemical treatment loses a part of electric charge supplied in secondary reactions in this final step... 

Arve and Liapis [34] suggest estimating the parameters characterizing the intraparticle diffusion and the adsorption-desorption step mechanisms of affinity chromatography from the experimental data obtained in a batch system. The numerical simulations of the chromatographic process will use the values of the parameters of the adsorption isotherm and those of the effective pore diffusion as determined from stirred tank experiments together with the film mass transfer coefficients calculated from chemical engineering expressions found in the literature. 

An orthogonal co-location method can be used to convert the above partial differential equahons (PDE) into the ordinary differential equations (ODEs). An ODE solver, EPISODE can be used to solve the (ODEs) (25). In the model, the diffusivity is obtained from a batch kinetic study while the external mass transfer coefficient can be calculated from empirical equations or is available in the literature. The longitudinal dispersion coefficient (D ) is determined by matching the model output with the experimental data. Readers may like to refer to Chen and Wang s work (9) for detailed information. 

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. 

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