Mass-transfer coefficients physical methods

An analysis of chemical desorption has recently been published (Chem.Eng.Sci., 21 0980)), which is based on a number of simplifying assumptions the film theory model is assumed, the diffusivities of all species are taken to be equal to each other, and in the solution of the differential equations an approximation which is second order with respect to distance from the gas-liquid interface is used this approximation was introduced as early as 1948 by Van Krevelen and Hoftizer. However, the assumptions listed above are not at all drastic, and two crucial elements are kept in the analysis reversibility of the chemical reactions and arbitrary chemical mechanisms and stoichiometry.The result is a methodology for developing, for any given chemical mechanism, a highly nonlinear, implicit, but algebraic equation for the calculation of the rate enhancement factor as a function of temperature, bulk-liquid composition, interface gas partial pressure and physical mass transfer coefficient The method of solution is easily gene ralized to the case of unequal diffusivities and corrections for differences between the film theory and the penetration theory models can be calculated. 

According to this method, it is not necessaiy to investigate the kinetics of the chemical reactions in detail, nor is it necessary to determine the solubihties or the diffusivities of the various reactants in their unreacted forms. To use the method for scaling up, it is necessaiy independently to obtain data on the values of the interfacial area per unit volume a and the physical mass-transfer coefficient /c for the commercial packed tower. Once these data have been measured and tabulated, they can be used directly for scahng up the experimental laboratory data for any new chemic ly reac ting system. 

Dl = diffusivity of transferring solute in liquid, m /sec If the diffusivity, Dl, needed for use in the above equations is not known, it can be estimated from data or methods given in the Perry s Chemical Engineers, Handbook (Section 14 in 4th Edition or Section 3 in 5th Edition). Note that the calculation of the mass transfer coefficients for a given regime involves only physical properties and is independent of agitation conditions. 

The aim of this paper is to make measurements with liquids of various physical properties in order to define the effect of the liquid properties and operating conditions on the parameter /q, and the limits of validity of the literature models for the interpretation of mass transfer coefficients in bubble dispersions. The method, which is used for the measurements, was verified in Part I to minimize misinterpretations. 

For development of nonequilibrium methods to continue, the calculations for mass transfer coefficients and interfacial areas required by these models will have to be added to physical property packages. Krishnamurthy and Taylor (89) present methods and recommendations for calculating the mass and energy transfer coefficients and rates. Help may be available from published manuals or supplier literature. 

In many practical applications, gas-liquid mass transfer plays a significant role in the overall chemical reaction rate. It is, therefore, necessary to know the values of effective interfacial area (aL) and the volumetric or intrinsic gas-liquid mass transfer coefficients such as kLah, kL, ktaL, kg, etc. As shown in Section IX, the effective interfacial area is measured by either physical e.g., photography, light reflection, or light scattering) or chemical methods. The liquid-side or gas-side mass-transfer coefficients are also measured by either physical (e.g., absorption or desorption of gas under unsteady-state conditions) or chemical methods. A summary of some of the experimental details and the correlations for aL and kLaL reported in the literature are given by Joshi et al. (1982). In most practical situations, kgaL does not play an important role. 

Gas-liquid mass transfer in the absence of solids has been widely studied (Shah et al, 1982). In these studies, both physical and chemical methods for the determination of the volumetric mass-transfer coefficient and the gas-liquid... 

The volumetric mass transfer coefficient is also determined for three-phase (gas-liquid-solid) systems using both physical and chemical methods described above. A summary of these studies is given in Table XXXII. 

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. 

The principle of the physical absorption technique we used, is based on the continuous observation of the absorption kinetics of a solute gas by following the total pressure in the gas phase of a stirred reactor closed to both phases (manometric method). This physical technique was first described by Teramoto et al. [1] these authors used it to determine the liquid side mass transfer coefficient k], a. This technique was then employed with success at high pressures and temperatures by different authors [1-6]. For this reason we have selected this method to determine the liquid side as well as the gas side mass transfer coefficient kGa. 

Experiments of physical absorption of C02 diluted with N2 into pure water allow to measure gas side mass transfer coefficients. In this case, we measure the total mass transfer resistance (liquid+gas), using the method for the kLa determination ( 3.1). Knowing the liquid resistance, we can then calculate the gas side one. The pressure of interest in this case is the partial pressure of C02, which is obtained by simultaneous measurements of total pressure and molar fraction of C02 versus time. 

The physical absorption technique (manometric method) is suitable to determine the liquid side volumetric mass transfer coefficient as well as the gas-side one. Results show that kLa is independant of pressure and depends mainly on the system s hydrodynamics and secondly, that koa is inversely proportional to the total pressure and can be related to the liquid Reynolds number. 

Cybulski and Moulijn [27] proposed an experimental method for simultaneous determination of kinetic parameters and mass transfer coefficients in washcoated square channels. The model parameters are estimated by nonlinear regression, where the objective function is calculated by numerical solution of balance equations. However, the method is applicable only if the structure of the mathematical model has been identified (e.g., based on literature data) and the model parameters to be estimated are not too numerous. Otherwise the estimates might have a limited physical meaning. The method was tested for the catalytic oxidation of CO. The estimate of effective diffusivity falls into the range that is typical for the washcoat material (y-alumina) and reacting species. The Sherwood number estimated was in between those theoretically predicted for square and circular ducts, and this clearly indicates the influence of rounding the comers on the external mass transfer. 

The result obtained from the film theory is that the mass transfer coefficient is directly proportional to the diffusion coefficient. However, the experimental mass transfer data available in the literature [6], for gas-liquid interfaces, indicate that the mass transfer coefficient should rather be proportional with the square root of the diffusion coefficient. Therefore, in many situations the film theory doesn t give a sufficient picture of the mass transfer processes at the interfaces. Furthermore, the mass transfer coefficient dependencies upon variables like fluid viscosity and velocity are not well understood. These dependencies are thus often lumped into the correlations for the film thickness, 1. The film theory is inaccurate for most physical systems, but it is still a simple and useful method that is widely used calculating the interfacial mass transfer fluxes. It is also very useful for analysis of mass transfer with chemical reaction, as the physical mechanisms involved are very complex and the more sophisticated theories do not provide significantly better estimates of the fluxes. Even for the description of many multicomponent systems, the simplicity of the model can be an important advantage. 

The basic aim of the method suggested here allows the engineer to express mass and momentum transfer data for a given system in terms of mass transfer coefficients that can be related to measurable physical parameters for a system. 

For the degree of conversion, and taking into account the ionized liqnid, the Henry s law coefficient is Hi = 2535 atm/m.f. = 45.63 atm/(kg moles/m ). Also, for the flow conditions given, the physical mass transfer coefficients, based on the method of Bolles and Fair, are... 

Mass transfer coefficients are experimentally determined by methods such as the one used in this example. They must then be correlated with the physical properties of the system, equipment geometry, and flow conditions if they are to be generally useful. Examples of such correlations are given later in the chapter. 

Use of symbolic drag coefficients (Section I1,C,2) and symbolic heat-and mass-transfer coefficients (Section IV, A) furnishes a unique method for describing the intrinsic, interphase transport properties of particles for a wide variety of boundary conditions. Here, the particle resistance is characterized by a partial differential operator that represents its intrinsic resistance to vector or scalar transfer, independently of the physical properties of the fluid, the state of motion of the particle, or of the unperturbed velocity or temperature fields at infinity. Though restricted as yet in applicability, the general ideas underlying the existence of these operators appear capable of extension in a variety of ways. 

The value of the mass transfer coefficient depends on the physical system, the transporting species, physicochemical properties of the fluid and the fluid flow rate. Methods of estimating mass transfer coefficients are given elsewhere (8-10). 

Experimental studies were carried out to derive correlations for mass-transfer coefficients, reaction kinetics, liquid holdup and pressure drop for the new catalytic packing MULTIPAK (see [9,10]). Suitable correlations for ROMBOPAK 6M were taken from [70] and [92], The vapor-liquid equilibrium is calculated using the modification of the Wilson method [9]. For the vapor phase, the dimerization of acetic acid is taken into account using the chemical theory to correct vapor-phase fugacity coefficients [93]. Binary diffusion coefficients for the vapor phase and for the liquid phase are estimated via the method purposed by Fuller et al. and Tyn and Calus, respectively (see [94]). Physical properties like densities, viscosities and thermal conductivities are calculated from the methods given in [94]. 

The liquid side volumetric physical mass transfer coefficient was determined from the desorption rate of oxygen. Detailed description of the experimental set up, procedure and analysis of data is given by Tosyali [30]. Methods of estimating the interfacial CO2 concentration, diffusivities of CO2 and OH in the liquid phase, reaction rate constant, which are all required in data analysis, can be found elsewhere [31, 32]. ... 

As already mentioned foe mass transfer coefficients used for calculations in chemical engineeting are rather parameters in foe calculation model than physical values. That is diy speaking of methods for determination of these coefficients we should distinguish methods for determination of foe mass transfer coefficients for foe piston flow model and for foe diffusion model. Since for foe latter model foese coefficients are connected with foe axial mixing coefficients in gas and liquid phase, foe methods for their determination are discussed after foe mefoods for determination of foe axial mixing coefficients. 

This chapter begins with a definition of the different transfer processes involved in chemical transport in the atmosphere-canopy-soil surface system. A qualitative description of each process is followed by an example of how the relevance of the different processes changes with the physical chemical properties of the chemical. Then, a theoretical framework is presented for the two processes for which this is available, namely dry gaseous deposition and dry particle-bound deposition. This is accompanied by a description of the measurement methods available to quantify these processes. The last section is devoted to summarizing the available correlations and presenting several example calculations of mass transfer coefficients. 

The steady-state model consists of a set of coupled ordinary differential and algebraic equations. The simulation is obtained by integrating simultaneously the mass-balance equations for the gas and liquid phases in the axial direction of the reactor using a fourth-order Runge-Kutta method. The heat balance is used only for the simulation of the industrial reactors. The solid phase algebraic equations are solved between integration steps with the Newton-Raphson method. Physical properties and mass-transfer coefficients are also updated in every integration step. 

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