Процессы массопереноса с участием твердой фазы. Учебное пособие

Coefficients of mass transfer and mass delivery with the index “v” are called volumetric. They are connected with the usual coefficients, which are referred to the surface of interfacial contact, with the help of simple relations, as it follows from (1.129) - (1.132):

βyV = βya, βxV = βxa, K yV = K y a, K xV = K xa (1.133)

Expressions of volumetric coefficients of mass transfer through the volumetric coefficients of mass delivery are similar to (1.105), (1.106), (1.110), (1.111). If the values of volumetric coefficients of mass delivery or mass-transfer are already known, then, depending on the formulation of the task, we can extremely easy determine the working volume of the apparatus V or the quantity of the substance, which moves from one phase

(1.132). At this case it is not necessary to solve a difficult task of defining the specific surface of the interfacial contact .

However, volumetric coefficients cannot be easily defined theoretically. It is difficult to obtain for them generalized equations with the help of the method of physical modeling too. You should pay attention to the dimensionality of volumetric coefficients of mass delivery and mass transfer. In the SI system they are measured in [s-1].

For calculating of apparatus with a stepped contact of phases, coefficients of mass delivery and mass transfer is more convenient to refer not to the volume of an apparatus, but to the area of the working section of a contact device f, for example, to the square of the working section of a plate. After defining the specific surface of contact of phases as af (interfacial surface, formed at the given contact device and referred to the

42

working section), we can write the equation of mass transfer in the

Similarly, you can rewrite and other equation (1.129)-(1.132) by using the factors of mass transfer and mass delivery, referred to the area of the working section of a contact device:

βyf = βyaf , βxf = βxaf , K yf = K yaf , K xf = K xaf (1.136)

Number and height of transfer units. Main geometrical parameter of the most common type of mass-transfer apparatus (cylindrical vertical columns), which depends on mass transfer rate, is the height of a device H. If the cross-sectional area of the machine S is constant, then its volume can be written as

This is another modification of the equation of mass transfer, also does not containing the interfacial surface value. Similarly, you can transform and the other equations (1.129) - (1.132):

43

The first cofactors of these equations is called the Height of Transfer Unit (HTU), and the second - the Number of Transfer Unit (NTU). Moreover, before a name of the value, characterizing the process of mass transfer (hoy, hox, noy, nox), is added the definition «total» («common»). The values, characterizing the process of mass delivery (hy, hx, ny, nx), are called «partial», or «phasic».

Number of units of transfer is the change of the working concentration of the phase in the limits of a part of an apparatus, relatively to the moving (driving) force of the process, averaged for this part. Then one unit of transfer corresponds to the part of the apparatus, for which the change of working concentration of the phase is equal to the average moving force in this division. Using expressions (1.125), (1.126) or (1.128) - (1.141), you can use many ways to provide total numbers of transfer units:

In case of possibility of calculation of the averaged moving (driving) force as an averaged logarithmic value, NTU can be easily obtained analytically. As coefficients of mass transfer are expressed through coefficients of mass delivery, total numbers of units of transfer could be expressed through the number of partial units of transfer. So, when m = const

44

conductivity Ki or effective diffusion coefficients Die , using them instead

of coefficient of molecular diffusion in the equations of the first (1.13) and the second (1.39) Fick's laws.

Mass-carry with the solid porous bodies participation is described similarly to the heat exchange. For the case of mass-carry in twocomponent mixtures differential equations of unsteady-state convective diffusion (1.37) and of thermal conductivity are identical. This allows to use the ratios, describing heat exchange, for the description of mass exchange in case of hydrodynamic similarity of the flows and identity of the initial and boundary conditions of heat and mass movements. In this case most convenient is to use the dimensionless ratios, in which the criteria of thermal (T) similarity Nu , Pr are simply replaced with the

diffusion criteria Nud , Prd .

Usage of equations of mass conductivity allows you, having replaced the thermal conductivity coefficient of λ on Ki, to applicate the thermal analogy to the description of mass transfer with a solid porous body. So, unsteady-state mass exchange with the boundary conditions of the third kind can be represented by analogy with the heat exchange in the form of

where ci is the concentration of the distributable components in the solid phase: ci (y, t) - in point y at time t, cio - in the initial moment of time; ci* - equilibrium with the concentration of component i in the nucleus of the flow; id , Fod - diffusion criteria of Bio and Fourier; δ - a characteristic

linear size. Dependences, presented in the reference literature for the heat exchange, can be also used for the mass exchange too.

Let's consider one more typical case of a mass exchange between a solid phase (gas or liquid) and distributed in it elements of disperse phase (solid particles). For dissolving solid particles, all resistance of mass flow is concentrated in the solid phase. The solution for spherical particles of small diameter, slowly moving relative to the solid phase (Red<<1), has been found in the approximation of the boundary layer [10]:

46

When Re → 0, i.e. for the state of the rest of particles, the expression (1.157) is not applicable, and in this case, Nug,d =2. With the increase of Re there can be observed the separation of a boundary layer even in the laminar regime, what does not allow to receive a theoretical solution in these conditions. Criteria equations, obtained by the method of physical modeling, are applicable over a much larger area (up to Red ~ 104) , but provide a more complicated dependence.

Mass exchange within the dispersed phase is non-stationary field of concentrations changes over time. But for spherical particles the task can be solved analytically:

CHAPTER 2. ADSORPTION AND ION EXCHANGE

2.1. General Information

Adsorption is a process of absorption of one or several mobile components from a fluid (gas, vapor-steam or liquid mixtures) by a solid absorber, called adsorbent. In this section the adsorption out of a gas phase will be considered, but all the arguments and relations, except (45), are applicable for the liquid mixtures as well.

Adsorbing substance, located in a gas (fluid) is called adsorptive; this substance after the transition to adsorbent phase becomes adsorbate.

Adsorption processes are selective and usually reversible. Due to their reversibility it is possible to separate the absorbed substances from adsorbent (desorption).

Adsorption is applied mainly to the low levels of the removing matter in the initial mixture, when it is necessary and possible to achieve almost complete extraction of the adsorptive. In those cases, when concentrations of the removing substances in the initial mixture is great, it is usually more profitable to use absorption.

In industry the adsorption processes are used in cleaning and drying of gases, in particular for removing of the volatile solvents vapors from

47

their mixtures with the help of air and other gases (recovery of volatile solvents).

The solid body ability to absorb a substance from the gas phase is due to the molecules particular properties on the solid body surface. Their force fields, in contrast to the force fields of molecules, located in the volume of a solid body in the midst of the other molecules, are not balanced. As the result, there appears the force, directed to the surface of a solid body (the force of attraction). So, the attraction of molecules from gas phase realizes under the action of this force. In accordance to the nature of the forces, acting on a solid body surface, adsorption can be distinguished to the physical and chemical adsorption. The last is usually called chemisorption.

The physical adsorption occurs under the action of forces of mutual attraction between gas molecules and the molecules on the surface of a solid body (Van-der-Waals forces). Van-der-Waals forces action is manifested at the distances considerably exceeding the gas molecules sizes. So, the multiple layers of absorbed molecules usually appear on the adsorbent surface just owing to the physical adsorption.

In case of the chemical adsorption, or chemisorption, the chemical bonds occur as the result of the chemical reactions between the absorbed gas molecules and the molecules on the adsorbent surface.

The most important adsorbent characteristics are: absorbing capacity and selectivity. We understand under the adsorbent absorbing capacity a quantity of the substance, which can be absorbed by its` mass or volume unit, and under the adsorbent selectivity we understand its` ability to absorb only the target component (or components) of the sharing gas mixture.

2.2. Types of Adsorbents and Their Characteristics

Porous solids with a large specific surface (attributed to a unit of substance mass) are usually used as adsorbents. Adsorbents have different (by the diameter) capillary channels - pores, which can be conditionally divided into: macropores (more than 2·10-4 mm), intermediate or mezopores (6·10-6 - 2·10-4 mm) and micropores (2·10-6- 6·10-6 mm). The nature of adsorption process is determined by the pores sizes.

Macropores specific surface is relatively small, so at their surface (at the walls) adsorb a small amount of substance. Macropores mainly play the role of the transport channels for gas molecules.

48

On the surface of the transition pores, which size is significantly more than the size of the adsorbing molecules, during the adsorption emerge the layers of the absorbed substance. It is possible the formation of layers with the different thickness from one molecule (monomolecular adsorption) up to a few molecules (polymolecular adsorption) .

Micropores dimensions are close to the sizes of molecules, and the adsorption in micropores leads to the filling of their volumes. That`s why, there is no meaning to speak about the formation of layers of absorbed substance on the surface of micropores. Usually the micropores are connected with macro - and transitional pores, and it reduces the way, which pass the adsorbed molecules, and leads to the adsorption acceleration.

Adsorbents are characterized by their sorption or adsorption capacity, determined by the concentrations of the absorbed substance in the unit of mass or volume of the adsorbent.

The absorbing capacity of the adsorbent in relation towards a concrete substance depends on the adsorption temperature and pressure, as well as on the concentration of the absorbed substance. The highest possible absorbing capacity of the adsorbent under the stated conditions is called the equilibrium activity.

Active coals and mineral adsorbents (silica gel, zeolites, etc.), as well as the synthetic ion-exchange resins (ionites), are mainly used in industry as adsorbents.

Active Coals. Porous active coals are produced by dry distillation of various coal containing substances (wood, bones, etc.) with the purpose of removal of volatile components and activation of produced coals for their porosity improvement. Specific surface area of active coal ranges from 600 to 1700 m2/g. The granule size of some standard brands of activated carbons for gases adsorption is 1-5 mm (BAU coal) and 1.5 - 2.7 mm (ACT coal). The bulk density of coals of these brands is equal to 260 and 420 kg/m3 respectively. Usage of coal of this or that kind depends on the varieties of adsorption process, in which they are used (absorption of gases, recovery of volatile solvents, etc.). The lack of active coals is their combustibility; they catch fire in the air at a temperature of about 300 0C.

Silica Gel. This is mineral adsorbent, representing a hydrated gel of silica acid (SiO2 x n·H2O), obtained by the action of sulfuric acid or salt solutions with a sour reaction, on the solution of sodium silicate. The gel, released after rinsing with water, is dried up to the final humidity of 5 - 7%, which corresponds to the largest adsorption ability. Silica gels stand out by

49

their homogeneity and uniform distribution of pores sizes, which medium diameters lie within the range from 1.5 to 5·10-6 mm. The specific surface of silica gel varies from 400 up to 770 m2/g. The granule size varies from 0.2 to 7 mm, the bulk density is 400 - 800 kg/m3.

Silica gels are mainly used for gas drying. The absorption capacity of silica gels in relation to the organic substances vapors reduces in the presence of moisture. Silica gels` advantages are incombustibility and more high (in comparison with active coals) mechanical strength.

Zeolites. These adsorbents are natural or synthetic minerals (aluminum silicates of alkali metals). Synthetic zeolites are primarily used as industrial adsorbents with rather homogeneous pores structure, which size is commensurate with molecule size. These zeolites are of molecularsieve action, which lies in their ability not to absorb molecules, having the size more than pores diameter.

Zeolites stand out by high sorption capacity with respect to water, and they are often used for deep dehydration of gases containing small amounts of moisture. The sizes of zeolite granules are from 2 to 5 mm.

2.3. Equilibrium in Adsorption

The amount of substance, absorbed by mass or volume unit of the adsorbent in achieving the state of equilibrium, in gas mixture depends on the temperature and concentration of the adsorbing matter. This relationship can be written as:

where a - the absorbed substance concentration in the adsorbent, equilibrium with its concentration in the gas-phase, kg adsorbate / m3 adsorbent; - is the concentration of the adsorptive in gas phase, kg of adsorptive / m3.

Concentration of the absorbing substance can be replaced by its partial pressure p in gas mixture. Then adsorption isotherm takes the form

Isotherms of adsorption (equilibrium) are determined empirically. Type of an adsorption isotherm depends on many factors: on the nature of the adsorbate and adsorbent, on specific surface of the adsorbent, on pores

50