# Mass transfer in the adsorption of impurities - Theoretical...

## Mass transfer in adsorption of impurities

Absorption capacity of adsorbents is expressed by the concentration of adsorbate in the mass or volume unit of the adsorbent. The adsorption process is accompanied by the release of heat, so reducing the temperature contributes to its conduct.

Equilibrium at adsorption. Regardless of the nature of adsorption forces, the following factors influence the amount of adsorption and the equilibrium of the process: the nature of the substance being absorbed; temperature; pressure; impurities in the phase from which the substance is absorbed.

The nature of the substance to be absorbed - it is considered that the equilibrium concentration in the adsorbent is higher, the greater the molecular weight of the absorbed gas, and in the case of solutions, the less the solubility of the substance absorbed in the liquid.

Adsorption accelerates when the temperature decreases or when pressure rises. The same factors influence the desorption process in the opposite direction. Desorption is accelerated by increasing the temperature of the adsorbent and decreasing the pressure, and also by passing through the adsorbent vapors that displace the absorbed substance.

Impurities in the phase from which the substance is absorbed - in the presence of a phase from which the adsorbent absorbs substance A, competing (displacing) substance B, i.e. substance, which is also capable of being absorbed by this adsorbent, the equilibrium concentration of substance A in the adsorbent decreases. In this case, substance B either partially or completely displaces or replaces substance A in the adsorbent.

With the passage of time, during adsorption, equilibrium sets in, which establishes a definite relationship between the concentration of the adsorbed substance X (kg/kg of adsorbent) and its concentration H in the gas phase:

(7.61)

where Y is the equilibrium concentration of the inert part of the gas mixture, kg/kg; A, n are coefficients determined experimentally (with n ≥ 1).

The dependence (7.61) of the adsorption of the target component under equilibrium conditions between phases at a constant temperature is called the adsorption isotherm. There are five types of physical vapor adsorption isotherms (Figure 7.9).

The isotherm shown in Fig. 7.9, a, corresponds to monomolecular Langmuir adsorption; the isotherms in Fig. 7.9, b, c - monomolecular and poly molecular adsorption. The isotherms shown in Fig. 7.9, d, q, correspond to the case when monomolecular and poly molecular adsorption are accompanied by capillary condensation.

Equation (7.61) can be represented in another form (since the concentration of a component in a gas mixture at a constant temperature is proportional to its pressure):

(7.62)

where A 1 is the coefficient; p is the equilibrium pressure of the absorbed substance in the vapor-gas mixture, Pa.

At high temperatures or small partial pressures, adsorption isotherms are approximated by Henry's law:

(7.63)

where - amount of absorbed substance, kg/kg (adsorbent) or kg/m; A p is the phase equilibrium constant; p i is the partial pressure of the component in the gas.

In practical calculations Freundlich's equation is widely used:

(7.64)

where A 1 and n are the coefficients.

For monomolecular physical adsorption, the Langmuir equation is used:

Fig. 7.9. Types of adsorption isotherms (a-d)

(7.65)

where b is the coefficient; a m is the limiting value of adsorption.

The Brunauer-Emmett-Teller equation (BET), which describes monomolecular and multilayer adsorption, has a universal character:

(7.66)

The absorbed molecules from the side of the surface of the adsorbent are acted upon by an attractive force proportional to the adsorption potential:

(7.67)

A serious deviation from the real characteristics of adsorption is the assumption of the isothermicity of the process. Adsorption can be isothermal only with the appropriate organization of the heat sink from the condensation zone. In other cases, the heat released during condensation of the adsorbate and wetting the surface of the adsorbent will go to heat the processed gas, adsorbent particles.

Material balance of the adsorption process. The adsorption processes are carried out periodically or, if the adsorbent moves through the apparatus, continuously. The material balance of such processes is expressed by an equation common to all mass transfer processes:

(7.68)

where G - the consumption of the vapor-gas phase; L - consumption of adsorbent; y - working concentrations of the adsorbed substance in the vapor-gas phase or solution; x - working concentrations of the adsorbed substance in the adsorbent.

Adsorption in a layer of a fixed adsorbent is a batch process in which the concentration of the absorbed substance in the adsorbent and in the vapor-gas phase varies with time and space.

The total material balance of the sorbed substance in the element during the time dt without taking into account the longitudinal mixing of the gas flow is expressed by the equation

(7.69)

Equation (7.69) is called the differential equation of the material balance of the periodic adsorption process in the layer of the stationary adsorbent.

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