Mass-transfer coefficients in adsorption

TABLE 16-9 Recommended Correlations for External Mass Transfer Coefficients in Adsorption Beds (Re = evdp/v. Sc = v/D)... 

In a typical pulse experiment, a pulse of known size, shape and composition is introduced to a reactor, preferably one with a simple flow pattern, either plug flow or well mixed. The response to the perturbation is then measured behind the reactor. A thermal conductivity detector can be used to compare the shape of the peaks before and after the reactor. This is usually done in the case of non-reacting systems, and moment analysis of the response curve can give information on diffusivities, mass transfer coefficients and adsorption constants. The typical pulse experiment in a reacting system traditionally uses GC analysis by leading the effluent from the reactor directly into a gas chromatographic column. This method yields conversions and selectivities for the total pulse, the time coordinate is lost. 

The selection of adsorbents is critical for determining the overall separation performance of the above-described PSA processes for hydrogen purification. The separation of the impurities from hydrogen by the adsorbents used in these processes is generally based on their thermodynamic selectivities of adsorption over H2. Thus, the multicomponent adsorption equilibrium capacities and selectivities, the multi-component isosteric heats of adsorption, and the multicomponent equilibrium-controlled desorption characteristics of the feed gas impurities under the conditions of operation of the ad(de)sorption steps of the PSA processes are the key properties for the selection of the adsorbents. The adsorbents are generally chosen to have fast kinetics of adsorption. Nonetheless, the impact of improved mass transfer coefficients for adsorption cannot be ignored, especially for rapid PSA (RPSA) cycles. 

The other subgroup of the lumped rate approach consists of the reaction dispersive model where the adsorption kinetic is the rate-limiting step. It is an extension of the reaction model (Section 6.2.4.3). Like the mass transfer coefficient in the transport dispersive model, the adsorption and desorption rate constants are considered as effective lumped parameters, kads,eff and kdes.eff- Since no film transfer resistance exists (Cpi = q), the model can be described by Eq. 6.79 ... 

Equation 6.87 shows that the lumped mass transfer coefficient in the solid fihn driving force model is related to the film mass transfer coefficient, the intraparticle diffusion, and the adsorption rate constant. This equation is a more complete form of Eq. 6.57b. It reduces to that equation when the adsorption-desorption kinetics is infinitely fast. 

Table 5 shows examples of LDF mass transfer coefficients for adsorption of several binary gas mixtures on BPL activated carbon particles (6-16 mesh) at 23-30°C. The data show that the mass transfer coefficients are relatively large for these systems. There is a scarcity of multicomponent adsorption equilibria, kinetics, and heat data in the published literature. This often restricts extensive testing of theoretical models for prediction of multicomponent behavior. 

Calculate volumetric overall mass-transfer coefficients in fixed-bed adsorption from correlations for the individual coefficients, and use them for breakthrough predictions. 

Mass Transfer Coefficient in Rapid Cyclic Adsorption and Desorption 267... 

You want to scale up an adsorption which, in a lab column 1 cm in diameter and 20 cm long, showed a breakthrough at 40 min and exhaustion at 52 min. Other experiments suggest that the unused bed length is about equal to an HTU, and you expect mass transfer coefficients in this bed to vary with the square root of the flow. In your new column, you must have 10,000 times greater capacity and a bed 130 cm long (to minimize pressure drop). You plan to increase the flow 17 times. What should the bed diameter be ... 

The effects of chemical reactions are exemplified by the data for ammonia adsorption in water summarized in Fig. 17.0-1. The overall mass transfer coefficient, in cm/sec, is based on a liquid side driving force given in mol/cm. The specific values shown are for a hollow-fiber membrane contactor, though similar values would be obtained in a packed tower or other more conventional apparatus. 

Although the adsorption of surfactants tends to reduce mass-transfer coefficients by suppressing drop circulation, a sharp increase in mass transfer... 

A pulse of a racemic mixture (5 g each enantiomer) was carried out to check the adsorption model and to predict the mass transfer coefficient. The other model parameters used in simulation were = 0.4 and Pe = 1000. The mass transfer coefficient used to fit experimental and model predictions in the pulse experiment was k = 0.4 s k Model and experimental results are compared in Figs. 9-16 and 9-17. 

In model equations, Uf denotes the linear velocity in the positive direction of z, z is the distance in flow direction with total length zr, C is concentration of fuel, s represents the void volume per unit volume of canister, and t is time. In addition to that, A, is the overall mass transfer coefficient, a, denotes the interfacial area for mass transfer ifom the fluid to the solid phase, ah denotes the interfacial area for heat transfer, p is density of each phase, Cp is heat capacity for a unit mass, hs is heat transfer coefficient, T is temperature, P is pressure, and AHi represents heat of adsorption. The subscript d refers bulk phase, s is solid phase of adsorbent, i is the component index. The superscript represents the equilibrium concentration. 

Here A(g) and B(g) denote reactant and product in the bulk gas at concentrations CA and Cg, respectively kAg and kBg are mass-transfer coefficients, s is an adsorption site, and A s is a surface-reaction intermediate. In this scheme, it is assumed that B is not adsorbed. In focusing on step (3) as the rate-determining step, we assume kAg and kBg are relatively large, and step (2) represents adsorption-desorption equilibrium. 

External mass transfer is the only process of the three involved in adsorption that can be predicted with reasonable accuracy from physical data. Mass transfer from the bulk gas to the particle surface can be considered by the film resistance approach. The rate of mass transfer is proportional to the external surface area of the adsorbent particles and the adsorbate concentration difference between the bulk gas and the particle external surface. The proportionality constant is the mass transfer coefficient, the reciprocal of the resistance to... 

In this section we deal with the following two approximations for adsorption uptake rate and how to go about calculation of the relationship between the mass transfer coefficients (k, kK) that appear and the solutions to diffusion problems. 

The Brunauer type I is the characteristic shape that arises from uniform micro-porous sorbents such as zeolite molecular sieves. It must be admitted though that there are indeed some deviations from pure Brunauer type I behavior in zeoHtes. From this we derive the concept of the favorable versus an unfavorable isotherm for adsorption. The computation of mass transfer coefficients can be accompHshed through the construction of a multiple mass transfer resistance model. Resistance modehng utilizes the analogy between electrical current flow and transport of molecular species. In electrical current flow voltage difference represents the driving force and current flow represents the transport In mass transport the driving force is typically concentration difference and the flux of the species into the sorbent is resisted by various mechanisms. 

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