Процессы массопереноса с участием твердой фазы. Учебное пособие

volume and the distribution in their (pores) sizes, as well as on the process temperature. As an example, Fig. 2.1 demonstrates typical forms of the adsorption isotherms of different substances, and Fig. 2.2 - the adsorption isotherms of one substance at various processing temperatures.

Adsorption is accompanied by the reduction of the partial pressure of the absorbing component of a gas mixture and by considerable heat release. Therefore, in accordance with Le-Chatelier principle, the amount of adsorbed substance increases with the temperature decrease and with the pressure increase. From this it follows, that the increase of temperature and atmospheric pressure have the negative impact on the adsorption process by promoting the desorption of the substance, which was absorbed by the adsorbent.

2.4. Kinetics of Periodic Adsorption

Periodic adsorption is the unsteady-state process of mass transfer between a flow of sharing gas mixture, containing the absorbing component (adsorbtive), and the stationary layer of adsorbent. In general case, this process is characterized as the consecutive mass transfer of the adsorptive molecules, which move from the nucleus of the flow to the surface of the adsorbent particles (external mass transfer), and from this surface - into interior volume of these particles (internal mass transfer). In some cases this process may be limited either by external, or by internal mass transfer stages.

Calculation of periodic action adsorbers is based on the regularities of changes in time of the degree of adsorbent saturation and of adsorptive

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concentration in gas phase in each cross-section of an adsorbent layer. This spatial - temporal distribution of the absorbing component between the phases can be presented as follows. At the entrance of gas flow (with constant initial adsorptive concentration Cin (kg/m3)) into the layer of fresh

adsorbent (with concentration of adsorbate a = 0) the adsorbing component begins to absorb the first layer of the adsorbent granules, then the second, third, etc. Sooner or later a lot of consecutive layers of the adsorbent particles are involved in this process, however, each subsequent layer is washed by the gas flow with the adsorptive concentration < in , because

of a part of adsorptive has been already consumed by the previous layers. After the utmost saturation, particles of the first layer become

disengaged from the absorption process, and gas with the concentration Cin begins to wash the particles of the second layer, then the third, etc. Thus, in the adsorbent layer of the height H gradually appear three zones (Fig. 2.3):

assumption about the gas phase motion, corresponding to the ideal displacement model:

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(2.4)

∂

ρ ∂t - rm = 0

(2.5)

C* = f3 (a)

(2.7) where ε - the porosity of the adsorbent granular layer, W - dummy speed of gas movement in the layer, rm – source (or sink) of mass, caused by adsorptive transfer from the gas phase into a solid, kV - volume masstransfer coefficient, ρbd (or ρ ) - bulk density of the adsorbent. The system

of differential equations with partial derivatives must be complemented by an appropriate initial and boundary conditions. Usually it is assumed, that the initial concentration of the adsorbate is equal to zero or to some residual after the regeneration value , and the threshold adsorbtive concentration in gas phase - equal to Cbd.

Analysis of the solution of the equations system (2.4) - (2.7) shows, that in case of the convex form of the adsorption isotherms ((2.2), Fig. 2.1) and of permanent values of the volume mass-transfer coefficient kV, during some period of time the formation of a stationary concentration profile ( ) (stationary front of adsorption) occurs, and then happens the profile` parallel transfer with a constant speed u (Fig. 2.4).

Fig. 2.4. Concentration profiles of an adsorptive C(x,t) during its passing through a layer of adsorbent

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Profile of concentration ( ,t) for a linear and, more over, for a concave adsorption isotherms, expands more and more in time, which does not allow to speak in these cases about the parallel transfer of a stationary front of adsorption.

For the calculation and analysis of the periodic action adsorbers the concept of skipping time tskt (time of the protective action of the layer) is used. It corresponds to adsorbers` working time, during which the adsorptive concentration at the output of adsorbent layer will be equal to a given maximum of the allowable skipping concentrations skc, after whose achievement it is necessary to terminate the process and produce the regeneration of the adsorbent. skc can be found by the solution of equations (2.4) - (2.7) system at ( ,tskt) = skc, which can be obtained either analytically (in case of linear form of the adsorption isotherm and K v = const ) or by numerical methods.

Average concentration in adsorbate` layer at the skipping momentd is called the dynamic activity or adsorbent capacity (Fig. 2.3), and d <

due to the fact, that the adsorbate concentration in finite layers of adsorbent is less than equilibrium one. To get the maximum value of skipping time, you can use the model of perfect equilibrium adsorption, in accordance with which is supposed the infinitely high rate of mass transfer ( k v → ∞ ) and extremely convex (stepped) adsorption isotherm. In this

case, each elementary layer of adsorbent shall be saturated with adsorbate to equilibrium value a*(Cin) and only then a next layer will be included in the work. Skipping will come only when the absorbent will become saturated with adsorbate up to a*(Cin).

Skipping time can be determined from the material balance

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Skipping time in the model of the ideal adsorption tskti will correspond to the saturation of a whole layer of the adsorbent, having the height

Actual skipping time (tskt) will be less than ideal, and for its calculation, instead of static activity (equilibrium adsorbate concentration), the dynamic activity is used:

More over, due to the finite rate of the mass transfer process, time delay (t0) of the protective action of the layer can be defined and used in the following form:

be also obtained from the material balance equation. Writing it for the frame of reference, moving with the adsorption front, we get

εCin + ρbd a * (Cin )

where Wtrue - the true speed of a gas flow in the adsorbent layer. The same solution for u can be obtained from the equations (2.4) - (2.7) system.

2.5. Continuous Adsorption

The processes of continuous adsorption are stationary processes and are carried out in the devices with the opposed motion of a gas and adsorbent (counter flow). For the calculation of such a stable process with the motion of a dense layer of the adsorbent the methods of calculation of

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the mass transfer between two phases (for example, of absorption) can be used in a simplified form. Denote as G and Ginert the mass consumption of the adsorbent and of the inert part of the gas flow respectively, as in,fin, - the initial, final and current adsorbate concentrations in the

absorbent, as in , fin , and - relative mass concentrations of the

adsorptive in inert gas; in this case the values of and must be taken for the same cross-section of a device (see fig 2.5).

where is the amount of component, absorbed by the adsorbent per a unit of time.

Material balance equation for the bottom part of the layer,

beginning from the section with concentrations values and C , will be written in the form:

Ga (a fin - a ) = Ginert ( in - )

Solving the last equation on a, we get

Fig. 2.5. Scheme of material flows Fig. 2.6. Scheme of the working and equilibrium lines

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Equation (2.16) describes the working line (line of the working concentrations 1 - 2) of adsorption process, shown in Fig. 2.6. Above the working line on the same figure is shown the equilibrium concentrations line (3) a = f ( ) .

From the equation of material balance (2.15) the minimum relative consumption of adsorbent can be determined, if we consider that a fin = a

, i.e. the final absorbent concentration has reached the equilibrium value, so

Working line for the minimum amount of adsorbent is shown in Fig. 2.6 as a dotted line (1 – 3).

Mass transfer equation for an elementary volume of a layer, having the height dH (Fig. 2.5), can be written in the form:

d M = Ginert dC = K v (C - C )dV = K v (C - C )SdH , (2.19)

where Kv - volume mass transfer coefficient, referred to the gas phase;

dV = SdH - an elementary volume of the device; S - cross-sectional area of the apparatus. Solving the equation (2.19) on dH, we have

and the required working height of the apparatus will be:

In relation (2.21) the integral expresses a number of transfer units, and the multiplier Ginert K v S - a height of transfer unit.

2.6. Desorption

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Machines, which are involved in the adsorption process, are called adsorbers. According to the adsorbent layer status in the device, the adsorbers can be divided into three groups: 1 - adsorbers with a stationary layer of an adsorbent (machines of periodic action); 2 - adsorbers with a fluidized layer of adsorbent; 3 - adsorbers with a moving dense layer of an adsorbent. The last two groups belong to the devices of continuous action.

Batch Adsorber with a Stationary Layer of Adsorbent. In Fig. 2.7 is presented a scheme of the apparatus with a stationary layer of adsorbent. Periodic processes are often carried out in four stages.

First stage is actually adsorption, i.e., saturation of the adsorbent by the absorbing component. Original gas mixture is supplied in block 1 of the apparatus through socket 2, passes through the layer of adsorbent 9, and purified gases go out through socket 3.

Second stage - desorption of absorbed component of the adsorbent. Filling of original gas mixture is terminated, and the device is supplied with water vapor through a bubbler 4. Vapor mixture of desorbed component and water is removed through socket 5. After desorption, the condensate of the water vapor is drained from the device through socket 6.

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Third stage is the drying of adsorbent. After overlapping of water vapor input and output, wet absorbent is dried by hot air, coming into the apparatus through the socket 2 and getting out of it through the socket 3.

Fourth stage is the cooling of adsorbent. After stopping of hot air input, the adsorbent must be cooled by cold air, which comes in through socket 2 and goes out through socket 3. The working cycle of the apparatus at the end of the fourth stage starts again from the stage of adsorption. Processes of loading and unloading of the adsorbent are produced periodically through the hatches 7 and 8.

In Fig. 2.8 is shown a timetable of working stages for two adsorbers of periodic action in the scheme of a device of continuous action:

Fig. 2.8. Working schedule of two adsorbers

In this case, actually adsorption time t must be equal to the sum of times of desorption stage td, drying stage tdr and cooling stage t0, i.e.

t = td + tdr + t0.

If the summary duration of stages of desorption, drying and cooling exceeds the duration of adsorption stage, then the continuity of plant`s work can be achieved by using a larger number of adsorbers.

Adsorber with a Fluidized Layer of Adsorbent. Fig. 2.9 shows a diagram of the device of continuous action with a fluidized layer of adsorbent. Adsorber works as follows. Initial gas mixture is supplied to the apparatus through a socket 5, passes through the gas distribution grate 2 and fluidized layer of adsorbent 8. Adsorbent absorbs adsorptive from gas mixture, and the cleaned gases enter separator 3, where they will be cleaned again from adsorbent particles, carried away by the gas flow; further the refined gases go out of the device through socket 4. Apparatus has been continuously fed by the fresh adsorbent on tube 6, and from it, as

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