Cr er2

, [6.45 x 1020 (o-2 + a2)+ 1.34 x 1028 (a3 + a])- 4.23 x 10 V] +

! [6.45 x 1020 (er3 + er4)+ 4.01 x 1028 (er2 + er2)+ 1.32 x 1036 (er3 + er3)-4.17 x 1012 <fi]

Relative to equilibrium thermodynamics, nonequilibrium thermodynamics is less studied by researchers [54-58], Especially, its application thereof in special distillation processes is a new thing. The aim of nonequilibrium thermodynamics analysis for special distillation processes is to interpret in what condition and/or why the process can take place, so as to substantially understand the essence and find the theoretical judging rule. At the same time, the mathematic model of entropy generation can be established for the guidance of energy saving, so as to realize decreasing entropy generation. As we know, in the actual operation, trays in the distillation column rarely, if ever, operate at equilibrium. That is to say, nonequilibrium thermodynamics in the most degrees reflects the real state. In the phase space, nonequilibrium thermodynamics is divided into the linear and non-linear ranges. The linear range is commonly studied because in this case the linear driving force equation is satisfied. But at some time for such special distillation processes as azeotropic distillation, adsorption distillation and extractive distillation, the separation ability of the separating agent is so weak as to make tray efficiency low due to the large liquid load on the tray. Undoubtedly, not only the vapor and liquid phases can't reach equilibrium, but also the actual composition is far away from the equilibrium composition. So under this condition the system isn't in the linear range of nonequilibrium thermodynamics, and the linear driving force equation isn't satisfied.

Here reactive extractive distillation with tray column is selected as an example. The results obtained may be applied to common extractive distillation. Moreover, it can deduce the similar results of nonequilibrium thermodynamics analysis for other special distillation processes in the same way.

In the reactive extractive distillation, it is assumed that there are four components^, B, S and E concerned, in which A (the heavy component) and B (the light component) are the components to be separated, S is the separating agent, and E is the resultant formed by the following reversible reaction and has a high boiling point:

According to the principle of nonequilibrium thermodynamics, entropy generation ratio per volume cr can be written as

= +1J> [" v(y)+- ^ n. v« + £ |>, (145)

where the right terms mean the contributions due to the influences of heat conduction, diffusion (free diffusion and forced diffusion), viscosity flow, chemical reaction, respectively. Each term is composed of two factors: one is related with the irreversible ratio; another is related with the driving force resulting in the corresponding "flow".

In most cases, there is no apparent pressure gradient, temperature gradient and velocity gradient so that the three terms in the right side of Eq. (145) can be neglected. On the other hand, chemical reaction rate between A and S is generally quick and chemical reaction equilibrium can arrive in a very short time. Therefore, the term, r®;> can als° t>e neglected. Thus, Eq. (145) is simplified as

where V/i( is the chemical potential gradient between the liquid bulk and vapor bulk.

In the reactive extractive distillation, the separating agent S is generally high-efficiency, and can apparently improve the relative volatility of B to A. Accordingly, the amount of the separating agent S used in the distillation column is greatly reduced, which leads to a high tray efficiency. So it is reasonable to assume that the system concerned is in the linear range of nonequilibrium thermodynamics, and the linear driving force equation is satisfied. The mass transfer rate J, of the components A, B. S and /' can be expressed as

J a =£nV(-^) + I12V(-^) + LnV(-^) + Ll4V(-^) (147)

JB = Z2|V(-^) + Z22V(-^) + Z23V(-^) + Z24V(-^) (148)

^ =i4lV(-^f) + I42V(-^f) + I43V(-^f) + Z44V(-^) (150)

By virtue of the characteristics of extractive distillation that the boiling point of component S is generally far greater than that of component A or B, the concentration of S in vapor phase is minute and close to zero. On the other hand, £ is a resultant and thus the composition in vapor phase is supposed to be zero. So it may be thought that

When the system reaches the steady-state of nonequilibrium thermodynamics, one obtains:

According to the force balance equation ^ J, = 0 >

When Eq. (152) is incorporated into Eqs. (147)-(150), the linear algebraic equation group describing the relationship of diffusion force and diffusion coefficient is:

For the above linear algebraic equation group, the main matrix D is:

D =

Lu

¿,2

Lu

A4

¿2]

L22

¿23

¿24

¿3.

¿32

¿33

¿34

¿4,

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