Reactive Mass Transfer

The standard molar Gibbs energy of solvation can also be derived from pure component data using spectroscopic information for determining solvatochromic parameters in respect of activity, basicity, polarity, etc. There exists a number of linear solvatochromic scales, the most widely used of which is the linear solvation energy relationship (LSER) devised by Kamlet and Taft [37, 38]. The Nernst distribution of solute i according to Kamlet is  

Vi is the molar volume of the solute (as a measure of the size of the cavity to accommodate the solute i in the solvent), d is an empirical parameter which takes also account for polarizability n, a and / characterize respectively the acidity or basicity which in general represents the ability to form hydrogen bonds, and the C s are solvent characteristics independent of the solute. Meyer and Maurer [39] used this equation for 30 systems (371 substances, 947 experimental distribution coefficients) to evaluate generalized solvent Cj parameters. 

This equation is quite accurate in comparison with group contributing methods [40] or other predictive LSER methods [41]. For compounds where the solvatochromic parameters are known, the mean absolute error in log Dy is about 0.16. It is usually less than 0.3 if solvatochromic parameters of the solute and solvent must be estimated according to empirical rules [42], In contrast to the prediction of gas-liquid distribution coefficients, which is usually easier, the LSER method allows a robust estimation of liquid-liquid distribution coefficients. However, these equations always involve empirical terms, despite their being physico-chemically founded thermodynamic models. However, this is considered due to the fundamental character of the solvatochromic scales. 

The mass transfer at the liquid-liquid interface is composed of diffusional, kinetic and convective elements. Most of these applications are concerned with the extraction 

ad denotes the adsorbed species and the bars indicate bulk organic species. The resulting governing kinetics equation is then [31]  

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Variables. This system belongs to the physical chemical energy, in which the basic quantity is the substance amount n (or mole number) with unit in moles. The effort is the chemical potential p and the flow is the substance flow 3 (see the table of variables in the case study abstract). The name substance flow comes from the span of behaviors that the physical chemical energy has, which is wider than the chemical reactivity. Mass transfer (convection, diffusion, etc.) is a phenomenon... 

The reaction of aqueous sodium cyanide with 1-bromooctane, shown in equation (27), is catalyzed by tri-n-butylphosphonium ions (61 n= 1, DF 0.17, 2% DVB) as shown in Scheme 24. Reaction rates in heterogeneous mixtures can be limited by mass transport steps as well as intrinsic reactivity. Mass transfer of the cyanide ion from water to the particle surface, mass transfer of the 1-bromooctane from organic liquid to the particle surface and intraparticle diffusion of both reactants from the particle surface to the active sites within the gel polymer are required. Reaction... 

R is rate of reaction per unit area, a is interfacial area per unit volume, S is solubiHty of solute in continuous phase, D is diffusivity of solute, k is rate constant, kj is mass-transfer coefficient, is concentration of reactive species, and Z is stoichiometric coefficient. When Dk is considerably greater (10 times) than Ra = aS Dk. 

The physical mass-transfer rate of o2one into water is affected by the gaseous o2one concentration, temperature, pressure, gas dispersion, turbulence, mixing, and composition of the solution, ie, pH, ionic strength, and the presence of reactive substances. Mass transfer of gaseous o2one into... 

With a reactive solvent, the mass-transfer coefficient may be enhanced by a factor E so that, for instance. Kg is replaced by EKg. Like specific rates of ordinary chemical reactions, such enhancements must be found experimentally. There are no generalized correlations. Some calculations have been made for idealized situations, such as complete reaction in the liquid film. Tables 23-6 and 23-7 show a few spot data. On that basis, a tower for absorption of SO9 with NaOH is smaller than that with pure water by a factor of roughly 0.317/7.0 = 0.045. Table 23-8 lists the main factors that are needed for mathematical representation of KgO in a typical case of the absorption of CO9 by aqueous mouethauolamiue. Figure 23-27 shows some of the complex behaviors of equilibria and mass-transfer coefficients for the absorption of CO9 in solutions of potassium carbonate. Other than Henry s law, p = HC, which holds for some fairly dilute solutions, there is no general form of equilibrium relation. A typically complex equation is that for CO9 in contact with sodium carbonate solutions (Harte, Baker, and Purcell, Ind. Eng. Chem., 25, 528 [1933]), which is... 

For physical absorption, values of the mass-transfer coefficients may not vary greatly, so a mean value could be adequate and coiild be taken outside the integral sign, but for reactive absorption the variation usually is too great. 

Engineering factors include (a) contaminant characteristics such as physical and chemical properties - concentration, particulate shape, size distribution, chemical reactivity, corrosivity, abrasiveness, and toxicity (b) gas stream characteristics such as volume flow rate, dust loading, temperature, pressure, humidity, composition, viscosity, density, reactivity, combustibility, corrosivity, and toxicity and (c) design and performance characteristics of the control system such as pressure drop, reliability, dependability, compliance with utility and maintenance requirements, and temperature limitations, as well as size, weight, and fractional efficiency curves for particulates and mass transfer or contaminant destruction capability for gases or vapors. 

Given a number Nr of waste (rich) streams and a number Ns of lean streams (physical and reactive MSAs), it is desired to synthesize a cost-effective network of physical and/or reactive mass exchangers which can preferentially transfer a certain undesirable species. A, from the waste streams to the MSAs whereby it may be reacted into other species. Given also are the flowrate of each waste stream, G/, its supply (inlet) composition, yf, and target (outlet) composition, yj, where i = 1,2,..., Nr. In addition, the supply and target compositions, Xj and x j, are given for each MSA, where j = 1,2, Ns. TTie flowrate of any lean stream, Ly, is unknown but is bounded by a given maximum available flowrate of that stream, i.e.. 

In order to establish the conditions for thermodynamic feasibility of reactive mass exchange, it is necessary to invoke the basic principles of mass transfer with chemical reactions. Consider a lean phase j that contains a set Bj = z —... 

We have covered a body of material in this chapter that deals with movement of mass along gradients and between phases. We have examined the commonalities and differences between linear driving forces, net rates of adsorption, and permeation. Each has the common feature that reaction is not involved but does involve transport between apparently well-defined regions. We move now to chemically reactive systems in anticipation of eventually analyzing problems that involve mass transfer and reaction. 

The transfer process is termed gas film controlling if essentieilly all of the resistance to mass transfer is in the gas film. This means that the gas is usually quite soluble in, or reactive with, the liquid of the system. If the system is liq-... 

Since the free energy of a molecule in the liquid phase is not markedly different from that of the same species volatilized, the variation in the intrinsic reactivity associated with the controlling step in a solid—liquid process is not expected to be very different from that of the solid—gas reaction. Interpretation of kinetic data for solid—liquid reactions must, however, always consider the possibility that mass transfer in the homogeneous phase of reactants to or products from, the reaction interface is rate-limiting [108,109], Kinetic aspects of solid—liquid reactions have been discussed by Taplin [110]. 

Example 11.8 With highly reactive absorbents, the mass transfer resistance in the gas phase can be controlling. Determine the number of trays needed to reduce the CO2 concentration in a methane stream from 5% to 100 ppm (by volume), assuming the liquid mass transfer and reaction steps are fast. A 0.9-m diameter column is to be operated at 8 atm and 50°C with a gas feed rate of 0.2m /s. The trays are bubble caps operated with a 0.1-m liquid level. Literature correlations suggest = 0.002 m/s and A, = 20m per square meter of tray area. 

Ultrasound can thus be used to enhance kinetics, flow, and mass and heat transfer. The overall results are that organic synthetic reactions show increased rate (sometimes even from hours to minutes, up to 25 times faster), and/or increased yield (tens of percentages, sometimes even starting from 0% yield in nonsonicated conditions). In multiphase systems, gas-liquid and solid-liquid mass transfer has been observed to increase by 5- and 20-fold, respectively [35]. Membrane fluxes have been enhanced by up to a factor of 8 [56]. Despite these results, use of acoustics, and ultrasound in particular, in chemical industry is mainly limited to the fields of cleaning and decontamination [55]. One of the main barriers to industrial application of sonochemical processes is control and scale-up of ultrasound concepts into operable processes. Therefore, a better understanding is required of the relation between a cavitation coUapse and chemical reactivity, as weU as a better understanding and reproducibility of the influence of various design and operational parameters on the cavitation process. Also, rehable mathematical models and scale-up procedures need to be developed [35, 54, 55]. 

The modeling of mass transport from the bulk fluid to the interface in capillary flow typically applies an empirical mass transfer coefficient approach. The mass transfer coefficient is defined in terms of the flux and driving force J = kc(cbuik-c). For non-reactive steady state laminar flow in a square conduit with constant molecular diffusion D, the mass balance in the fluid takes the form... 

The derivation and experimental verification of the MMHS model represented a significant accomplishment and a natural plateau for film models. To be sure, there are general criticisms of film models and more specific criticisms of the MMHS model [6], However, overall the MMHS model should be recognized as a robust but simply applicable model which serves to demonstrate how factors such as intrinsic solubility of the acid drug, ionization and pA of the drug, and concentration of the reactive base all contribute to increasing the dissolution rate and mass transfer. 

Lin R, Zhang J, Bai Y (2006) Mass transfer of reactive crystallization in synthesizing calcite nanocrystal. Chem Eng Sci 61(21) 7019-7028... 

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