Feasible split

Application of Feasibility Diagram Column Feasible Split... 

Figure 4.12(b) illustrates the feasible split for the feed composition Xf2 Pure HOAc is chosen as the bottom product and the corresponding Damkohler number is Da = 5.68. The predicted split and the simulation results are compared in Fig. 4.8(b) and Tab. 4.2. 

Table 4.2. Comparison of mole iractions predicted from the feasible split algorithm and from the simulation.

Feasible split prediction Simulation Feasible split prediction Simulation ... 

In this chapter, we describe an algorithm for predicting feasible splits for continuous single-feed RD that is not limited by the number of reactions or components. The method described here uses minimal information to determine the feasibility of reactive columns phase equilibrium between the components in the mixture, a reaction rate model, and feed state specification. This is based on a bifurcation analysis of the fixed points for a co-current flash cascade model. Unstable nodes ( light species ) and stable nodes ( heavy species ) in the flash cascade model are candidate distillate and bottom products, respectively, from a RD column. Therefore, we focus our attention on those splits that are equivalent to the direct and indirect sharp splits in non-RD. One of the products in these sharp splits will be a pure component, an azeotrope, or a kinetic pinch point the other product will be in material balance with the first. 

Solutions of (6.14) and (6.15), the rectifying and stripping cascade flash trajectories, can be represented in mole fraction space (three dimensional for the IPOAc system). However, we represent the solutions in transformed composition space, which is two dimensional for IPOAc system (for a derivation and properties of these transformed variables [46]). This transformed composition space is a projection of a three dimension mole fraction space onto a two dimensional transformed composition subspace for the IPOAc system. Even though the correspondence between real compositions and transformed compositions is not one-to-one in the kinetic regime, we will make use of these transforms because of ease of visualization of the trajectories, and because overall mass balance for reactive systems (kinetically or equilibrium limited) can be represented with a lever rule in transformed compositions. We use this property to assess feasible splits for continuous RD. 

Note that calculating the flash trajectories at (f> = 0.5 does not provide the entire feasible product regions for continuous RD, but instead generates a subset of the feasible products. Selecting an iterate on the stripping cascade trajectory as a potential bottoms and an iterate on the rectifying cascade trajectory as a potential distillate does not guarantee that these products can also be obtained simultaneously from a RD column. This is simply because these product compositions may not simultaneously satisfy the overall mass balance for a reactive column. However, when the flash trajectories are used in conjunction with the lever rule for a continuous reactive column, the feasible splits for continuous RD can be quickly predicted. 

Our main purpose is to understand which column sequences can be used in order to get the necessary products. This task is called the task of sequencing (synthesis). The sequencing task is being solved in consecutive order beginning with the first distillation column, where initialn-component mixture comes to. For each column, it is necessary to determine feasible splits. 

The question about feasible splits is one of the principal questions in the distillation theory. The understanding of this question was gradually transformed and became more precise. 

Let s call the above-stated method of determination of the set of feasible splits at R = 00 and A = 00 the method of product simplex. 

Feasible Splits at R = oo and N = oo Table 3.2. Azeotropes for wood pyrolysis product... 

The rule of product simplex gives us the instrument that allows not only to determine feasible splits in the first column, but also gives an opportunity to determine at once the compositions of the products in the sequence of (n - 1) columns. Compositions corresponding to the vertexes of the product simplex the feed point belongs to can be obtained as columns system products. 

How to determine which minimum energy is necessary for the separation of any multicomponent mixture at any feasible split ... 

State the feasible splits for the equimolar mixture of acetone(l), benzene(2), chlo-roform(3), and toluene(4). For each spht, determine the necessary tray numbers and liquid and vapor flow rates in the top and bottom sections of the column at optimal location of the feed tray and optimal distribution of the component and reflux excess coefficients and product purities as in item 1. 

For azeotropic mixtures, the main difficulty of the solution of the task of synthesis consists not in the multiplicity of feasible sequences of columns and complexes but in the necessity for the determination of feasible splits in each potential column or in the complex. The questions of synthesis of separation flowsheets for azeotropic mixtures were investigated in a great number of works. But these works mainly concern three-component mixtures and splits at infinite reflux. In a small number of works, mixtures with a larger number of components are considered however, in these works, the discussion is limited to the identification of splits at infinite reflux and linear boundaries between distillation regions Reg° . Yet, it is important to identify all feasible splits, not only the spUts feasible in simple columns at infinite reflux and at linear boundaries between distillation regions. It is important, in particular, to identify the spUts feasible in simple columns at finite reflux and curvilinear boundaries between distillation regions and also the splits feasible only in three-section columns of extractive distillation. 

The theory of trajectory bundles described in Chapters 5 and 6 ensures the possi-bihty of identification of all feasible splits of multicomponent azeotropic mixtures. The software for synthesis of separation units for multicomponent azeotropic mixtures should include, besides the module of identification of feasible splits, a module of preliminary selection of these splits (i.e., choice of the most interesting splits, a module of determination of necessary recycle flow rates, a module of choice of entrainers, and also modules entering into the system of synthesis for zeotropic mixtures). 

In this system of equations, the unknown parameters ai, ai,..., Om are proportional to the distance from point (xi, X2,... x ) to the corresponding vertexes of possible product composition simplex. If all parameters ai,a2,...,ak obtained from Eq. (8.12) turn out to be positive, the potential product point being checked belongs to the possible product composition simplex under consideration otherwise, it does not belong to it. A similar method was used before to determine feasible splits at infinite reflux (Petlyuk, Kievskii, Serafimov, 1979) (see Chapter 3). 

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