Reversible distillation intermediate section trajectories

Figure 4.19. Reversible intermediate section trajectories of sharp auto-extractive distillation ofideal ternary mixture ( fi > K2 > K3) (a) D < E, and (b) D > E. Component 1, overhead prodnct component 3, entrainer x and y, composition in arbitrary cross-section x j), composition of psendoprodnct.

Figure 4.23. Reversible intermediate section trajectories for extractive distillation of four-component mixtures (a) mixture 1,2 is overhead product, and component 4 is en-trainer (b) component 1 is overhead product, and mixture 3,4 is entrainer. Short segments with arrows, liquid-vapor tie-lines in arbitrary cross-sections.

This allows us to actively influence the location of the pseudoproduct point of the intermediate section in order to maintain sharp separation (i.e., separation at which the intermediate section trajectory ends at some boundary element of the concentration simplex). This is feasible in the case when inside concentration simplex there is one trajectory of reversible distillation for pseudoproduct point x ) that ends at mentioned boundary element, and there is the second trajectory inside this boundary element. To maintain these conditions, pseudoproduct point x j) of the intermediate section should be located at the continuation of the mentioned boundary element, because only in this case can liquid-vapor tie-hues in points of reversible distillation trajectory located in this boundary element he at the lines passing through the pseudoproduct point x jy. We discuss these conditions in Chapter 4. It was shown that in reversible distillation trajectory tear-off point x[ev e from the boundary element the component absent in it should be intermediate at the value of the phase equUibrium coefficient between the components of the top product and of the entrainer rev,D > Kevj > Kev.s)- This condition is the structural condition of reversible distillation trajectory tear-off for the intermediate section. Mode condition of tear-off as for other kinds of sections consists of the fact that in tear-off point the value of the parameter (LfV) should be equal to the value of phase equilibrium coefficient of the component absent at the boundary element in tear-off point of reversible distillation trajectory ((L/V)m =... 

Intermediate section trajectory tear-off point x should lie on the reversible distillation trajectory in the boundary element Reg g (x e Reg g ) farther from pseudoproduct point x/, than all tear-off points x. g from it of reversible distillation trajectories into adjacent boundary elements. 

The dimensionality of intermediate section trajectory bundle is equal to n -m + 1, where n is total number of components, and m is summary number of components of top product and entrainer. Pseudoproduct point is located at the continuation of the boundary element, formed by all the components of the top product and entrainer. Reversible distillation trajectories and the stationary points are located at the mentioned pseudoproduct boundary element and at all boundary elements whose dimensionality is bigger by one (at m = n — 1, they are located inside concentration simplex). 

Figure 6.11. About calculation minimum entrainer flow rate E/D)ram- Ki, j and E/D as functions x j (a,b,c, respectively) for extractive distillation of the acetone(l)-water(2)-methanol(3) azeotropic mixture. x[ j = x g concentration of component 1 in tear-off point of intermediate section reversible distillation trajectory on side 1-2 Ki, phase equilibrium coefficient of component i in point j, x), j and E/D, concentration of component 1 in pseudoproduct point and ratio of entrainer and overhead flow rates, respectively, if tear-off point of intermediate section trajectory xj j on side 1-2 coincide with point...

In both cases, the trajectory tear-off point of sharp reversible distillation in the intermediate extractive section should lie at side 1-3 and the trajectory of intermediate section is a line, which is a geometric locus of points where the straight lines passing through a given point of pseudoproduct are tangent to residue curves. This trajectory reaches side 1-3 at the tear-off point and vertex 2 is the node... 

This result also remains valid for azeotropic mixtures. A necessary condition for exhausting of the some component in the intermediate (extractive) section at reversible distillation consists of the fact that the whole trajectory of intermediate (extractive) section should be located in the region where this component is intermediate in phase equilibrium coefficient (in the region of reversible distillation of the intermediate section Reg J. The segment of the side containing only the component separated as top product and component brought in as an entrainer is a boundary element of this region Reg l. ... 

Let s examine now the structure of trajectory bundles of sharp reversible distillation for the intermediate (extractive) section of the column with two feedings at separation of different types of azeotropic mixtures, the way we did it for the top and the bottom sections (Fig. 4.21). While composing these diagrams, we used, just as we did before, the data on the phase equilibrium coefficients of present and absent components at the sides of the concentration triangle and the general regularities of the location of the trajectory bundles of sharp reversible distillation. 

I. Define the main notions (1) region of reversible distillation of top Reg g bottom Reg -e, and intermediate sections Reg g (2) regions of trajectory tear-off Reg and Reg (3) region of possible product points of sharp reversible distillation Reg, Reg, and Reg and (4) node of trajectory bundle of reversible distillation Nrev-... 

Usage of nonadiabatic columns (i.e., column with intermediate at height inputs or outputs of heat), broadens conditions of separability of mixtures, having two reversible distillation traj ectory tear-off points. If, for example, heat is brought and drawn off in feed cross-section (Fig. 5.36), as it was offered in the work (Poellman Blass, 1994), then it is possible in one of the sections of the column, where there is limitation at the value of the parameter L/V or V/L, to keep the corresponding allowed value of this parameter, and joining of trajectories of the sections can be maintained at the expense of increase of vapor and liquid flows in the second section (Petlyuk Danilov, 1998). In a more general case, when there are limitations of the values of the parameters L/V and V/L in both sections, it is possible to use intermediate inputs and outputs of heat in the middle cross-sections of both sections. 

In the mode of minimum reflux adiabatic sections trajectories intersect reversible distillation trajectories in points Therefore, the separation process between product point and point can be carried out in principle, maintaining phase equilibrium between meeting flows of vapor and liquid in the cross-section at the height of the colunm by means of differential input or output of heat. We call such a separation process, with the same product compositions as at adiabatic distillation, a partially reversible one. A completely reversible process is feasible only for the preferable split that is rarely used in practice. Nonadiabatic distillation used in industry is a process intermediate between adiabatic and partially reversible distillation. Summary input and output of heat at nonadiabatic and adiabatic distillation are the same, and the energetic gain at nonadiabatic distillation is obtained at the transfer of a part of input or output heat to more moderate temperature level, which uses cheaper heat carriers and/or coolants. 

Liquid flows saltatory increases or decreases in the points of intermediate output or input of heat at the temperature 7 and The minimum possible value of hquid flows at parts from column ends to the points of intermediate input and output of heat is equal to the value of liquid flow at partially reversible process in those cross-sections, where Trev = T n rev = Calculation of reversible distillation trajectory at parts from column ends to points Sr and Ss determines the function L v =f l/T) for these parts and then determines such optimal values opt and opt 7, at which summary cost of inputs and outputs energy is minimum. Such an approach was introduced in the work (Terranova Westerberg, 1989 Dhole Linnhoff, 1993) and was named pinch method. ... 

Minimum values of the parameters L/V)r and (y/L)s in the feed cross-section of the column and compositions at trays above and below this cross-section x/ i and Xf at adiabatic and nonadiabatic distillation remain the same. The stationary points Sr and Ss also coincide, but at parts of reversible distillation trajectories between column ends and stationary points Sr and Ss the additional stationary points and Nf"-, corresponding to the points of intermediate inputs and output of heat (Fig. 6.2a), appear. 

As in that case, to develop a general algorithm of calculation of minimum reflux mode for columns with several feed inputs, we need to understand the location of reversible distillation trajectories of intermediate sections and the structure of trajectory bundles for these sections. 

Location of Reversible Distillation Trajectories of Intermediate Sections... 

Locations of reversible distillation trajectories depends on position of pseudoproduct point (i.e., on compositions and on flow rates of feeds and of separation products, as is seen from Eq. [6.3]). Difference from the top and bottom sections appears, when the pseudoproduct point of the intermediate section is located outside the concentration simplex (i.e., if concentrations of some components x j)i obtained from Eq. [6.3], are smaller than zero or bigger than one), which in particular takes place, if concentration of admixture components in separation products are small components (i.e., at sharp separation in the whole column). The location of reversible distillation trajectories of the intermediate sections at x j i < 0 or x, > 1 differs in principle from location of ones for top and bottom sections, as is seen from Fig. 6.3 for ideal three-component mixture (Ki > K2 > K3) and from Fig. 6.4 for ideal four-component mixture (Ki > K2 > K3 > K4). 

Figure 6.3. Reversible distillation trajectories of ideal ternary mixtures K > K2 > K3) for intermediate section of two-feed column (a) <0 ...

At nonsharp distillation in the intermediate section, as in top and bottom sections, there is only one reversible distillation trajectory, but in the intermediate section it has two node points Nrev in vertexes of concentration simplex, and in the top and bottom sections it has one node point in one vertex. 

In Chapter 5, we saw that the distillation process in a column section is feasible only if there are reversible distillation trajectories inside concentration simplex and/or at several of its boundary elements, because only in this case a section trajectory bundle with stationary points lying at these trajectories of reversible distillation arises in concentration simplex. This condition of feasibility of the process in the section has general nature and refers not only to the top and the bottom, but also to intermediate sections. Therefore, pseudoproduct points can... 

In contrast to nonsharp separation in the top and bottom sections, the intermediate section has at reversible distillation trajectory not just one node stationary point, but there are saddle point Sm and node point Nm- Separatrixes of the saddle points Sm divide concentration triangle into four regions Reg t trajectory bundles of intermediate section, one of which is the working one Reg jj,t-... 

At sharp adiabatic distillation in the intermediate section, several components may be absent at the pseudoproduct boundary element at which section trajectory ends, and the structural conditions of reversible distillation trajectory tear-off into all the adjacent boundary elements having dimensionality bigger by one should be valid in the trajectory tear-off point x[ from the boundary element >... 

Figure 6.7 shows for comparison the trajectories of quasisharp (a) and sharp (b) reversible distillation in the intermediate section for ideal mixture (Ki > K2> K3). This figure shows that, at movement of pseudoproduct point from the vicinity of continuation of side 1-3 to this continuation itself, there is transformation of reversible distillation trajectory it disintegrates into two parts - into one that lies inside the triangle and into the part that lies at side 1-3. We note that similar transformation also takes place at passage from quasisharp distillation to sharp one for the top and bottom sections. The stationary point Sm at this transformation stays at the internal part of reversible distillation trajectory. Point N+ passes to side 1-3. Point N passes from vertex 3 to its vicinity at side 1-3. 

We express the value of the parameter (E/D) through limit conditions when the point of tear-off of reversible distillation trajectory coincides with the saddle point of trajectory bundle of the intermediate section (e.g., = Sm at Fig. 

In the stationary points of the trajectory bundle of the intermediate section, the liquid-vapor tie-lines should be directed to pseudoproduct point of this section that is, in the given case, the point of water phase from decanter xli = Such quasistationary point is point qSm, where the calculated trajectory of the intermediate section changes its direction sharply, and the compositions at neighboring trays are very close to each other (quasizones of constant concentrations), and stationary point Af+ that coincides with the point of ternary heteroazeotrope and stationary point N that coincides with the point of binary azeotrope benzene(l)-isopropanol(2). Point Sm is located at reversible distillation trajectory of the intermediate section joining mentioned points N and Its location at this trajectory... 

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