Gases equimolar counterdiffusion

Equimolar Counterdiffusion in Binary Cases. If the flux of A is balanced by an equal flux of B in the opposite direction (frequently encountered in binary distillation columns), there is no net flow through the film and like is directly given by Fick s law. In an ideal gas, where the diffusivity can be shown to be independent of concentration, integration of Fick s law leads to a linear concentration profile through the film and to the following expression where (P/RT)y is substituted for... 

Multicomponent Diffusion. In multicomponent systems, the binary diffusion coefficient has to be replaced by an effective or mean diffusivity Although its rigorous computation from the binary coefficients is difficult, it may be estimated by one of several methods (27—29). Any degree of counterdiffusion, including the two special cases "equimolar counterdiffusion" and "no counterdiffusion" treated above, may arise in multicomponent gas absorption. The influence of bulk flow of material through the films is corrected for by the film factor concept (28). It is based on a slightly different form of equation 13 ... 

Equimolar Counterdiffusion. Just as unidirectional diffusion through stagnant films represents the situation in an ideally simple gas absorption process, equimolar counterdiffusion prevails as another special case in ideal distillation columns. In this case, the total molar flows and are constant, and the mass balance is given by equation 35. As shown eadier, noj/g factors have to be included in the derivation and the height of the packing is... 

Xm are not. For unimolecular diffusion through stagnant gas = 1), and reduce to T and X and and reduce to and equation 64 then becomes equation 34. For equimolar counterdiffusion = 0, and the variables reduce tojy, x, G, and F, respectively, and equation 64 becomes equation 35. Using the film factor concept and rate equation 28, the tower height may be computed by... 

First, consider the gradient of cA. Since A is consumed by reaction inside the particle, there is a spontaneous tendency for A to move from the bulk gas (cAg) to the interior of the particle, first by mass transfer to the exterior surface (cAj) across a supposed film, and then by some mode of diffusion (Section 8.5.3) through the pore structure of the particle. If the surface reaction is irreversible, all A that enters the particle is reacted within the particle and none leaves the particle as A instead, there is a counterdiffusion of product (for simplicity, we normally assume equimolar counterdiffusion). The concentration, cA,at any point is the gas-phase concentration at that point, and not the surface concentration. 

Based on such analyses, which of course do imply a film model in which the resistance to mass transfer is supposed to be confined to a film of finite thickness (see Volume 1, Chapter 10), it is possible to estimate the effect which mass transport external to the solid surface has on the overall reaction rate. For equimolar counterdiffusion of a component A in the gas phase, the rate of transfer of A from the bulk gas to the interface can be expressed as ... 

The right-hand side of equation 3.60 contains the mass transfer coefficient hD which is used if the driving force is expressed in terms of gas concentrations. Because of the stoichiometric demands imposed by chemical reaction, equimolar counterdiffusion of components may not necessarily occur and the effects of bulk flow must be taken into account (see Volume 1, Chapter 10). 

These relations imply that the mole fraction, iriplar concentration, and the partial pressure of either gas vary linearly during equimolar counterdiffusion. 

Properties The diffusion coeflicient of helium in air (or air in helium) at normal atmospheric conditions is Dgg = 7.2 x 10 m% (Table 14-2). The molar masses of air and helium are 29 and 4 kg/kmol, respectively (Table A-1). Analysis This is a typical equimolar counterdiffusion process since the problem involves two large reservoirs of ideal gas mixtures connected to each other by a channel, and the concentrations of species in each reservoir (the pipeline and the atmosphere) remain constant. 

A packed-bed distillation column is used to adiabatically separate a mixture of methanol and water at a total pressure of 1 atm. Methanol—the more volatile of the two components—diffuses from the liquid phase toward the vapor phase, while water diffuses in the opposite direction. Assuming that the molar latent heat of vaporization is similar for the two components, this process is usually modeled as one of equimolar counterdiffusion. At a point in the column, the mass-transfer coefficient is estimated as 1.62 x 10-5 kmol/m2-s-kPa. The gas-phase methanol mole fraction at the interface is 0.707, while at the bulk of the gas it is 0.656. Estimate the methanol flux at that point. 

Equimolar counterdiffusion can be assumed in this case (as will be shown in a later chapter, this is the basis of the McCabe-Thiele method of analysis of distillation columns). Methanol diffuses from the interface towards the bulk of the gas phase therefore, yM = 0.707 and yA1 = 0.656. Since they are not limited to dilute solutions,... 

Equimolar Counterdiffusion of a Binary Gas Mixture. Helium and nitrogen gas... 

In equimolar counterdiffusion, + Mbz = 0 in a binary gas mixture so is Under other conditions, the bulk velocity 0 the corresponding expressions ofMAz and the various mass-transfer coefficients will be developed now. The only restriction is that the magnitude of the transfer rate of species A is low. Consider again isobaric conditions and no external forces. From flux expression (3.1.94) and the relation (3.1.97),... 

One could also develop an analysis based on individual film coefficients, as we have done in equations (8.1.62(a)-d). Further, if the film coefficient/overall coefficient available is based on equimolar counterdiffusion, then a correction using the bulk flow correction factor has to be used for gas absorption/stripping therefore the expression for NTU will contain additional terms via... 

In the derivation of Eqs. (4.2.25) and (4.2.28) it was assumed that mass transport within the pores of the solid occurs by equimolar counterdiffusion. This should be a reasonable approximation for systems where there is a volume change on reaction, provided there is an excess of inert constituents present. A net generation of gas molecules (e.g., C + O2 ->2CO) results in an outward flow of gaseous products and reduces the rate of diffusion of the reactant into the solid. A net consumption of gas molecules (e.g., 2H2 + C ->CH4) results in the opposite effect. 

Let US consider an infinitesimally thin section of a fixed bed reactor through which a reactant gas is flowing, as sketched in Fig. 7.15. In an isothermal regime and for equimolar counterdiffusion, the system may be de-... 

The dimensionless representation of the reaction between a gas and a porous solid in a packed bed arrangement under isothermal conditions is helpful because it provides a convenient means for estimating the behavior of many reaction systems. However, the majority of systems encountered in practice are likely to be a great deal more complex in that neither the assumption of isothermal conditions nor the postulate of equimolar counterdiffusion (i.e., no change in the molar flow rate) are likely to be acceptable. 

General Situation. Both unidirectional diffusion through stagnant media and equimolar diffusion are idealizations that ate usually violated in real processes. In gas absorption, slight solvent evaporation may provide some counterdiffusion, and in distillation counterdiffusion may not be equimolar for a number of reasons. This is especially tme for multicomponent operation. 

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