Mass transfer coefficients for adsorption

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. 

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. 

Cooney, D. O. 1991. Determining External Film Mass Transfer Coefficients for Adsorption Columns. AIChE Journal 37 (8) 1270-1274. 

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. 

It was shown I8 that the binding process is the rate-limiting step, with an adsorption rate constant of kd = 4.8 x 104 dm mol s. The calculated mass transfer coefficient for the diffusion into the pores of the support contributes 11% to the overall adsorption process. The value of ka is an order of magnitude lower than that reported in Table 2. The binding properties of the polyclonal immunoadsorbents used in these two studies may differ because of the different methods employed for protein immobilization. Another possible explanation may be an underestimation of the contribution for the diffusion rate-limiting step as the polyclonal anti-HSA antibody was attached to a silica matrix of large pores [18]. 

In many industrial reactions, the overall rate of reaction is limited by the rate of mass transfer of reactants and products between the bulk fluid and the catalytic surface. In the rate laws and cztalytic reaction steps (i.e., dilfusion, adsorption, surface reaction, desorption, and diffusion) presented in Chapter 10, we neglected the effects of mass transfer on the overall rate of reaction. In this chapter and the next we discuss the effects of diffusion (mass transfer) resistance on the overall reaction rate in processes that include both chemical reaction and mass transfer. The two types of diffusion resistance on which we focus attention are (1) external resistance diffusion of the reactants or products between the bulk fluid and the external smface of the catalyst, and (2) internal resistance diffusion of the reactants or products from the external pellet sm-face (pore mouth) to the interior of the pellet. In this chapter we focus on external resistance and in Chapter 12 we describe models for internal diffusional resistance with chemical reaction. After a brief presentation of the fundamentals of diffusion, including Pick s first law, we discuss representative correlations of mass transfer rates in terms of mass transfer coefficients for catalyst beds in which the external resistance is limiting. Qualitative observations will bd made about the effects of fluid flow rate, pellet size, and pressure drop on reactor performance. 

Air at 294 K and 1 atm enters a fixed-bed adsorber at a flow rate of 0.146 m3/s with a benzene vapor concentration of 29 g/m3. The cylindrical adsorber is 0.61 m in inside diameter and is packed to a height of 1.83 m with 331 kg of silica gel particles having an effective diameter of 2.6 mm and an external porosity of 50%. The adsorption isotherm for benzene has been determined experimentally and found to be linear over the concentration range of interest, given by q = kc, where q is in kg benzene/kg gel, c is in kg benzene/m3 of gas, and k = 4.127 m3 of gas/kg of gel. It has been estimated that the overall volumetric mass-transfer coefficient for the conditions prevailing in the bed is Kc.a = 8.79 s-1. Assuming isothermal and isobaric operation, calculate ... 

Use experimental breakthrough data to estimate the volumetric overall mass-transfer coefficient for fixed-bed adsorption. 

Permeation flux through membrane Reaction rate constant for i-th reaction Bubble-to-cloud phase mass transfer coefficient for component I in cell n Bubble-to-emulsion phase mass transfer coefficient for component i in cell n Cloud-to-emulsion phase mass transfer coefficient for component i in cell n Adsorption constant for CO Equilibrium constant for y-th reaction... 

Coefficients of mass transfer resistance for adsorption layer columns (using Goiay s equation H= B/u + Cg+C /di. 

Equation (85) was later eonfirmed experimentally by Bohle and van Swaaij (1978), who measured mass transfer coefficients for a number of adsorbing (e.g., propane) and nonadsorbing (e.g., helium) gases in a fluidized bed of silica-alumina. A typical comparison is shown in Fig. 8, where the effect of adsorption is obvious with the enhancement being as high as 100%. 

Boltzmann s constant (3.1.72), (3.3.90c) rate constants for adsorption and dissociation, respectively (4.1.77a) backward and forwcud reaction rate constants (5.4.42) mass-transfer coefficient of species A in organic or water phase mass-transfer coefficients for species i (3.1.139), (3.4.3)... 

You need to estimate an overall mass transfer coefficient for solute adsorption from an... 

You need to estimate an overall mass transfer coefficient for solute adsorption from an aqueous solution of density 1.3 g/cm into hydrogel beads 0.03 cm in diameter. 

You have been recovering an antibiotic from a fermentation broth by adsorption on activated carbon and have found that the mass transfer coefficient for this adsorption is 6.1 10 cm/sec. In an effort to accelerate this adsorption, you switch to a cation-exchange resin of the same size beads and keep all details of your experiment the same. You find that the coefficient is now 1.03 10 cm/sec. Because this coefficient is highly temperature-dependent, you suspect that it is influenced by chemical reaction. The... 

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. 

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. 

The rate parameters of importance in the multicomponent rate model are the mass transfer coefficients and surface diffusion coefficients for each solute species. For accurate description of the multicomponent rate kinetics, it is necessary that accurate values are used for these parameters. It was shown by Mathews and Weber (14), that a deviation of 20% in mass transfer coefficients can have significant effects on the predicted adsorption rate profiles. Several mass transfer correlation studies were examined for estimating the mass transfer coefficients (15, jL6,17,18,19). The correlation of Calderbank and Moo-Young (16) based on Kolmogaroff s theory of local isotropic turbulence has a standard deviation of 66%. The slip velocity method of Harriott (17) provides correlation with an average deviation of 39%. Brian and Hales (15) could not obtain super-imposable curves from heat and mass transfer studies, and the mass transfer data was not in agreement with that of Harriott for high Schmidt number values. 

Transport to the electrode surface as described in Chapter 5 assumes that this occurs solely and always by diffusion. In hydrodynamic systems, forced convection increases the flux of species that reach a point corresponding to the thickness of the diffusion layer from the electrode. The mass transfer coefficient kd describes the rate of diffusion within the diffusion layer and kc and ka are the rate constants of the electrode reaction for reduction and oxidation respectively. Thus for the simple electrode reaction O + ne-— R, without complications from adsorption,... 

Because of their structural and conformational complexity, polypeptides, proteins, and their feedstock contaminants thus represent an especially challenging case for the development of reliable adsorption models. Iterative simulation approaches, involving the application of several different isothermal representations8,367 369 enable an efficient strategy to be developed in terms of computational time and cost. Utilizing these iterative strategies, more reliable values of the relevant adsorption parameters, such as q, Kd, or the mass transfer coefficients (the latter often lumped into an apparent axial dispersion coefficient), can be derived, enabling the model simulations to more closely approximate the physical reality of the actual adsorption process. 

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